Magnetic Behaviors of Mg- and Zn-Doped Fe3O4 Nanoparticles

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Article 3

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Magnetic Behaviors of Mg and Zn doped FeO Nanoparticles Estimated in Terms of Crystal Domain Size, Universal Dielectric Response and Application of FeO/CNTs composites to Anodes for Lithium Ion Batteries 3

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Zhongyuan Lv, Qi Wang, Yuezhen Bin, Ling Huang, Rong Zhang, Panpan Zhang, and Masaru Matsuo J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b07580 • Publication Date (Web): 21 Oct 2015 Downloaded from http://pubs.acs.org on October 29, 2015

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The Journal of Physical Chemistry

Magnetic Behaviors of Mg and Zn doped Fe3O4 Nanoparticles Estimated in Terms of Crystal Domain Size, Universal Dielectric Response and Application of Fe3O4 /CNTs Composites to Anodes for Lithium Ion Batteries

Zhongyuan Lv,1) Qi Wang,2) Yuezhen Bin,1,3) Ling Huang,2) Rong Zhang,4) Panpan Zhang, 1) and Masaru Matsuo*1,3) 1)

Department of Polymer Science and Material, Dalian University of Technology, Dalian 116024, China 2)

Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China

3)

State Key Laboratory of Fine Chemicals, Dalian University of Technology, Dalian 116024, China 4)

School of Material Science and Engineering, Hubei University of Technology, Wuhan 430068, China *Corresponding Author Email Address: [email protected] (M. M.) Tel/Fax: +86 411 84986093

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ABSTRACT

Magnesium (Mg) doped Fe3O4 nanoparticles representing as

MgxFe3-xO4 ( 0 < x ≤ 1 ) was analyzed in comparison with zinc (Zn) doped Fe3O4, ZnxFe3-xO4. Magnetization versus applied magnetic field for MgxFe3-xO4 particles provided the maximum saturation magnetization (Ms) with 69.37 emu/g at x = 0.1 as super-paramagnetism, while the Ms by Zn-doping was 80.93 emu/g at x = 0.2. The crystal unit volume (Vc) by Mg-doping at x ≤ 0.5 was constant but the crystal size decreased with increasing x. Doping beyond x = 0.6 provided small amorphous power aggregates which offer universal dielectric response implying highly disordered system. In contrast, the Vc by Zn-doping expanded up to x = 0.4 as the acceptable limit, which was attributed to the large difference between doping ion radius and replaced Fe3+ ion radius. On the other hand, the MgxFe3-xO4 ( 0 ≤ x < 0.6 ) and ZnxFe3-xO4 ( 0 ≤ x ≤ 0.4 ) formed by a crystal domain were analyzed by a three-circuit model with one normal parallel circuit and two circuits with resistance and constant phase element (CPE). The stability of capacity as anode of lithium ion batteries was investigated for the composites prepared by adhering Mg2+, Zn2+ and Fe3+ on sidewalls of as-modified multiwall carbon nanotubes. Among the ferrite composites, Zn0.2Fe2.8O4 provided the highest capacity with good stability under discharge and charge cycles.


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INTRODUCTION In the previous paper,1 a series of zinc (Zn) doped Fe3O4 nanoparticles with different Zn concentrations representing as ZnxFe3-xO4 ( 0 < x ≤ 1 ) was synthesized by the chemical co-precipitated technique mainly in the presence of sodium dodecyl benzene sulfonate (SDBS) as one of surface modifiers. Vibrating sample magnetometer (VSM) measurements provided that saturation magnetization (Ms) of ZnxFe3−xO4 achieved a maximum value of 80.93 emu/g at Zn0.2Fe2.8O4 (x = 0.2) and then decreased with increasing applied magnetic field.1 The performance of the magnetization was attributed to two factors. One was the super-exchange interactions among magnetic ions in the face-centred cubic inverse-spinel structure. Another factor was that the calculated results by modified Laue function fit very well with the experimental data. The WAXD results provided that the a-axis increased when the corresponding crystal size decreased with increasing x up to 0.4. When x exceed 0.4, it showed the inverse relationship and this indicated that x = 0.4 was Zn doping limit to form Zn doped Fe3O4 crystal structure. Due to the super-paramagnetism, Fe3O4 nanoparticle have already made substantial progress in many applied fields such as pigment,2 magnetic fluids,3 catalysts,4 microwave absorption materials,5 lithium ion batteries,6-7 magnetic resonance imaging (MRI),8 bioseparations,9 drug delivery,10 and other biomedical applications.11 It’s well known that the super-paramagnetism12, in which the residual magnetism (Mr) and the coercivity (Hc) are both close to zero13-15, depends on the crystal structure and domain size. When the particle size of Fe3O4 becomes smaller than the critical diameter (Dc < 128 nm), the residual magnetism (Mr) and the Hc are both close to zero.13-15 On the other hand, when the particle size of Fe3O4 becomes smaller than Dc,16-17 the magnetic 3 ACS Paragon Plus Environment


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materials present super-paramagnetism. But the saturation magnetization (Ms) value for Fe3O4 nanometer micro-particles was about 50 emu/g

15, 18-19

, which was lower

compared with the Ms of the bulk ferroferric oxide (85-100 emu/g).11, 20 In order to increase the Ms value for Fe3O4 nanometer micro-particles, inverse-spinal ferrite materials have been prepared, in which the Fe3O4 was doped by multifarious divalent metallic elements including Zn, Co, Ni, Ba, Cu and Mn.21-25 Magnetism for Fe3O4 roots in the indirect interactions among the cations in inverse-spinel structure in which oxygen ions (O2-) are arranged to form face-centered cubic (FCC) lattice where there are two kinds of sub-lattices, namely tetrahedral (A-site) and octahedral (B-site) interstitial sites,

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and in which the super-exchange interactions occurred.

11, 27, 28

Metallic ion-dopant influenced super-exchange interactions which are sensitive to the category and the location of metallic ions and thus changed the magnetic property of the material. Based on the results obtained for ZnxFe3-xO4 crystal,1 magnesium (Mg) was used in this study to avoid the damage of Fe3O4 crystals instead of Zn2+ with a radius of 74 pm, because the radius (65 pm) of Mg2+ ion in the A-site is almost equal to that of replaced Fe3+ ion (64 pm). The doping mechanism was mainly discussed based on the results of VSM and WAXD in comparison with the previous results for Zn doping. The Ms of MgxFe3-xO4 was maximum (69.37 emu/g) at x = 0.1 and the value was close to 73.54 emu/g for Zn doping at x = 0.1.1 With increasing x, however, the crystal size became smaller drastically and became very small powder aggregates with no appearance of WAXD peak beyond x > 0.6, which was also estimated by the complex permittivity ( ε * ). The plateau (dull) of the real part ( ε ' ) at low frequency and a broad peak of the imaginary part ( ε " ) indicated universal dielectric response (UDR) reflecting highly 4 ACS Paragon Plus Environment

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disordered system by heavy doping. On the other hand, the MgxFe3-xO4 ( 0 ≤ x < 0.6 ) and ZnxFe3-xO4 ( 0 ≤ x < 0.4 ) formed by a crystal domain were analyzed by a three-circuit model with one normal parallel circuit and two circuits with resistance and constant phase element (CPE), which provided good agreement between experimental and theoretical results. Furthermore, the stability of capacitance as anode of lithium ion batteries by using Mg2+, Fe2+ and Fe3+ was investigated by adhering Mg2+, Zn2+ and Fe3+ on sidewalls of as-modified multiwall carbon nanotube (MWCNT), in which poly(vinylalcohol) (PVA) was adopted as a hydrogen bond functionalizing agent to modify MWCNTs. The adoption of Zn0.2Fe2.8O4 furnished highest capacitance and best stability under discharge and charge cycles. The reason was analyzed in terms of a crystal unit volume size. The present work shall shed light on a number of applications of ferrite nanocomposites to the industrial field in near future.

EXPERIMENTAL SECTION Sample preparation Synthesis of MgxFe3-xO4 nanoparticles. Magnesium-doped Fe3O4 particles represented as MgxFe3-xO4 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0) series were prepared by the chemical co-precipitation method. Typically, appropriate pure powders of hexahydrated ferric chloride (FeCl3•6H2O), tetrahydrated ferrous chloride (FeCl2•4H2O) and hexahydrated magnesium chloride (MgCl2•6H2O) were dissolved in distilled water and thoroughly mixed to get homogeneous solution under a nitrogen atmosphere. The detailed process was similar to that shown in previous paper.1

Preparation of ferrite-MWCNTs nanocomposites. The ferrite/MWCNTs nanocomposites were prepared by in situ synthesizing ferrite nanoparticles with the 5 ACS Paragon Plus Environment


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same chemical co-precipitation method in the presence of carbon nanotubes (MWCNTs, VGCF-X, SDK Co. Ltd) and polyvinyl alcohol (PVA). Firstly, MWCNTs with a diameter of ca. 15 nm and a length of ca. 3 µm were treated by stirring the MWCNTs in a mixture of sulfuric acid/nitric acid (3:1 by volume, respectively) at 75 oC for 2 h and then were washed by distilled water until pH reached 7. After being dried for 12 h under vacuum, the MWCNTs were added into the 2.5 wt% PVA aqueous solution and the suspension was stirred as well as ultrasonic treated for 1 h to promote the dispersal of MWCNTs. After then, with the aforementioned chemical co-precipitation method, ferrite nanoparticles were synthesized on the surface of MWCNTs and PVA was adopted as a coupling reagent in the process. Then the product was purified by distilled water and ethanol. The ferrite/MWCNTs nanocomposites were stabilized by heating them to 280 oC at a rate of 1 oC/min and keeping for 1 h under N2. After that, for advanced crystallization of ferrite and carbonization of PVA, the stabilized nanocomposites were heated up to 500 oC at a rate of 3 oC/min under N2 and sustained for 2 h. Based on the type of doped metal, three kinds of ferrite/MWCNTs were synthesized: Fe3O4/MWCNTs, Zn0.2Fe2.8O4/MWCNTs and Mg0.6Fe2.4O4/MWCNTs. The schematic diagram for the fabrication of the ferrite/MWCNTs composites was shown in Figure 1.


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Figure 1.

Schematic diagram for the fabrication of the ferrite/MWCNTs composites7

Preparation of the lithium ion battery. The electrodes of ferrite/MWCNTs nanocomposites were prepared by dispersing 80 wt% active materials, 10 wt% polyacrylic latex binder (LA132) and 10 wt% acetylene black in water solvent to form a homogeneous slurry. The slurry was spread onto a copper foil and then was dried at 100 o

C under vacuum for 12 h. The cell was made from a ferrite/MWCNTs nanocomposites

cathode and a lithium anode. The electrodes were separated by a separator film (Celgard 2400). The electrolyte reservoir was made from LiPF6 (1 M) in a mixture of ethylene carbonate (EC)/dimethyl carbonate (DMC)/diethyl carbonate (DEC) 1:1:1 (vol%), which were provided by Guangzhou Tinci Materials Technology Co. Ltd.

Characterization Wide angle X-ray Diffraction (WAXD) for the samples were performed by a D/max-2400 X-ray generator (Rigaku), in which WAXD intensity measurements were carried out with a step interval of 0.02°, ranging from 20 to 70° with a divergent slit of 0.5 mm. The X-ray instrument was operated using Cu Kα radiation (λ = 0.1542 nm) at l50 mA and 40 kV. A transmission electron microscope (TEM) (JEM-1010) was used to observe the morphology of the samples at a voltage of 100 kV. The high resolution transmission 7 ACS Paragon Plus Environment


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electron microscopy (HR-TEM) images and selected area electron diffraction (SAED) were performed by using TEM, JEOLJEM-2100 microscope at a voltage of 200 kV. A vibrating sample magnetometer (JDM-13) was used to measure the magnetic field dependent magnetization up to 9000 Oe at room temperature. The frequency dependence of complex impedance was measured using a Solartron Impedance/Gain phase Analyzer (SI1260 + 1296). The nanoparticles were molded under compression. The area and thickness of each resultant film were ca. 0.2827 cm2 and 0.0361 ~ 0.0545 cm, respectively, and the detailed values were represented in Supporting Information (SI) 1. The inner plate of Cu electrodes, which was contacted with a resultant film, was coated by Au using an ion coater. Ag paste was coated on the surfaces of a ferrite film and those of the composite. Typical oscillation voltage was set to be 0.1 V, since the scattered values of complex impedance against frequency were the smallest. The measured frequency was in the range from 10-1 to 106 Hz. The atomic elements of doped Fe3O4 particles were analyzed by an energy dispersion X-ray spectrometry (EDS) (Oxford Instruments X-Max) together with a scanning electron micrographs (SEM) at 20 kV . A battery test system (NEWWARE BTS-610, Neware Technology Co. Ltd.) was used to investigate the electrochemical property of the cells with a current density of 200 mAg-1 for a cut-off voltage of 0.02-3.0 V (versus Li+/Li) at room temperature. Raman experiments were performed using 632.8 nm excitation line from He-Ne gas laser with a laser power about 1.2 mW on the sample surface. To shorten the paper, the results were shown in SI 2.


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RESULTS AND DISCUSSION The EDS result was shown in Figure 2. As shown in Figure 2a~d, the mass ration of magnesium and iron (Mg/Fe) increased with increasing of the doping ration (x) indicating the doping was accomplished. The ratio of Mg/Fe increased to 0.211 when x was 0.6 which was similar to the previous results for Zn/Fe.1 Inductively coupled plasma emission spectrometer (ICP-ES) (Optima 2000 DV, Perkin Elmer) was applied to study content of the iron element in the ferrite-MWCNT nanocomposites and the content of ferrite was obtained by a simple calculation which was shown in Table S2 in SI3.

Figure 2.

EDS spectra measured for MgxFe3-xO4 at the indicated molar ratio x

Figure 3a shows magnetization curves by the VSM for MgxFe3-xO4 powders with different Mg2+ contents. The Ms at x > 0.6 was almost zero. It is seen that the curves of



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MgxFe3-xO4 were similar to those of ZnxFe3-xO4: the curves went through the origin reversibly with negligibly small hysteresis, and the values of residual magnetism (Mr) and coercivity (Hc) were very small. The values of Mr and Hc were listed in Table S3 in SI 4. Compared with ZnxFe3-xO4, there were two different behaviors for MgxFe3-xO4. The first was that the magnification for the MgxFe3-xO4 powders increased linearly up to 400 Oe, and it levelled off beyond 4000 Oe, whereas those values for ZnxFe3-xO4 were 500 Oe and 2000 Oe, respectively, as shown in Figure 3a and 3c. The MgxFe3-xO4 and ZnxFe3-xO4 reached a saturated condition basically at 9000 Oe and 4400 Oe, respectively. The second one was that Ms of MgxFe3-xO4 reached the highest value at x = 0.1, and the Ms of Mg0.1Fe2.9O4 was 69.37 emu/g. But, the highest Ms for ZnxFe3-xO4 was 80.93 emu/g at x = 0.2. Judging from the behavior of Ms values and negligible hysteresis loop, the resultant MgxFe3-xO4 are super-paramagnetism similar to that of ZnxFe3-xO4.13-15 Figure 3b shows the curves of M/Ms(0) for MgxFe3-xO4 at H ≥ 0, which are normalized by Ms of Fe3O4 at 9000 Oe. The results reveal that the Ms provides the maximum value at x = 0.1 and the value at x = 0.2 is almost equal to that at x = 0. The value of Ms decreases with increasing x drastically and the Ms becomes zero beyond 0.6. In this case, the diffraction from the (311) plane of Fe3O4 becomes a very broad curve similar to the scattering from an amorphous halo. This phenomenon shall be discussed later in Figure 4a. The reason why Ms at x = 0.2 is almost equal to Ms at x = 0, shall be also discussed later by using schematic diagram by replacement of Fe3+ ions with Mg2+ ions in terms of super-exchange and double-exchange interactions in Figure 11a.


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Figure 3.

Field-dependent magnetization of MgxFe3-xO4 and ZnxFe3-xO4 with

different Mg2+ and Zn2+. (a) Original curve for MgxFe3-xO4. (b) Normalized curves by Ms(0) at 9000 Oe. (c) Original curve for ZnxFe3-xO4.1 (d) Normalized curves by Ms(0) at 4400 Oe.1

To facile understanding the different magnetic behaviors between MgxFe3-xO4 and ZnxFe3-xO4, the results for ZnxFe3-xO4 are shown as Figure 3d again in the present paper. The value of 80.93 emu/g for ZnxFe3-xO4 is not only far higher than that of Fe3O4 but also is almost the highest among inverse-spinel ferrite materials

21-25

except Cu-Zn

ferrites whose magnetization is beyond 100 emu/g but provides measurable hysteresis loop.24 The further difference between Mg doping and Zn doping is due to the fact that the magnetization versus applied magnetic field for MgxFe3-xO4 at x ≥ 0.3 is drastically lower than the original Fe3O4 (x = 0) , while Ms values for ZnxFe3-xO4 at x ≥ 0.3 are 11 ACS Paragon Plus Environment


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higher than Ms of Fe3O4 (x = 0) as shown in Figure 3d. This reason was discussed already in terms of double-exchange interaction.1 It should be noted that Ms was up to the maximum for Mg0.1Fe2.9O4 at x = 0.1, when a very small amount of Fe3+ was replaced by Mg2+, while the maximum Ms occurred for Zn0.2Fe2.8O4 at x = 0.2 (see Figure 3c). In the previous paper,1 the main cause concerning the maximum Ms for Zn0.2Fe2.8O4 could be resolved by the variation of crystal structure as well as double-change and super-exchange interactions. By using the same concept and additional experiments concerning dielectric properties, the main cause for Mg01.Fe2.9O4 shall be analyzed and the difference between MgxFe3-xO4 and ZnxFe3-xO4 shall be discussed in detail later in Figures 4-11. Figure 4a shows XRD intensity distributions for MgxFe3-xO4 with different Mg2+ contents. The diffraction peaks of MgxFe3-xO4 at x = 0 ~ 0.5 appeared approximately at the same positions as those of pure Fe3O4 (x = 0) as shown in Figure 4a. This indicates that the nanoparticles have the same length of the a-axis of crystal unit with face-centered cubic inverse-spinal structures.28 The peaks were indexed six crystal planes, corresponding to (220), (311), (400), (422), (511) and (440), respectively.30 Among them, the strongest peak is from the (311) plane. However, the peak becomes indistinct with increasing x. That is, the strongest peak from the (311) plane becomes a very broad peak similar to the scattering from highly disordered system like amorphous phase. With further increase beyond 0.6, the peak of the (311) plane disappeared. In contrast, XRD intensity distribution for ZnxFe3-xO4 nanoparticles with different Zn contents is shown in Figure 4c, which was shown already elsewhere1 but is shown again to compare with the diffraction from MgxFe3-xO4. Different from MgxFe3-xO4 nanoparticles, the angles of diffraction peak from ZnxFe3-xO4 decreased with increasing 12 ACS Paragon Plus Environment

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x up to 0.4 but increased inversely beyond 0.4, indicating that x = 0.4 is a critical content of Zn. This was attributed to the change of the a-axis’s length corresponding to the expansion of the crystal unit beyond 0.4. The expansion is probably thought to be the different atomic size of Fe3+ (64 pm) and Zn2+ (74 pm). If this is the case, the replacement of Fe3+ (64 pm) with Mg2+ (65 pm) provides no change of peak shifts because of similar atomic size. To justify no peak shifts in spite of changing x, the structural variation of the crystal unit was investigated by using the (311) plane with the strongest peak.

Figure 4.

(a) WAXD intensity distribution of MgxFe3-xO4 for the indicated x. (b)

Enlargement for the (311) plane diffraction. (c) WAXD intensity distribution of ZnxFe3-xO4 for the indicated x.1 (d) Enlargement for the (311) plane diffraction.1



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Figure 4b reveals the enlargement for peak profile for the (311) plane. The very small peak shift could be evaluated by using such methods that Poisson’s ratio of polyethylene crystal31 and crystal modulus along the chain axes for several crystalline polymers such as polyethylene,32-33 polypropylene,34-35 poly(vinyl alcohol),36 nylon 6,37 and poly(ethylene terephthalate)38 and cellulose I and II crystals39 have been measured. That is, the deviation of peak position for MgxFe3-xO4 was estimated as that of the center of gravity of the intensity distribution function represented by the eq 1 in Ref 1 and the results are listed in Table 1.

Table 1.

The results of the crystal domains of MgxFe3-xO4 D311 (nm)

label

β(O)

2θmax(O)

D (nm) d(nm)

a(nm)

(Scherer

N (Laue Function)

Equation)

x=0

0.79

35.46

0.2532

0.8398

10.48

39

9.87

x = 0.1

0.85

35.46

0.2532

0.8398

9.75

36

9.11

x = 0.2

0.90

35.42

0.2534

0.8405

9.16

34

8.62

x = 0.3

0.91

35.42

0.2534

0.8405

9.03

34

8.62

x = 0.4

1.04

35.46

0.2532

0.8398

7.94

29

7.34

x = 0.5

1.14

35.46

0.2532

0.8398

7.23

26

6.58

Table 1 reveals that the peak top remained at the same angle. It indicates that d between the (311) planes maintain the same distance by no change of the a-axis, as listed in Table 1 together. The detailed evaluation justifies that the replacement of Fe3+ (64 pm) with Mg2+ (65 pm) did not change the crystal size because of the similar atomic 14 ACS Paragon Plus Environment

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sizes. However, the intensity becomes lower with increasing x and the peak from the (311) plane disappeared. The replacement of Fe3+ with Mg2+ in A-site and the decrease of the number of Fe2+ in B-site (see Figure 11a) caused drastic disruption of crystallites by the powerless super-exchange interaction between A- and B- sites and powerless double-exchange interaction in B-site. The average crystal number decreased from 39 to 26 up to x = 0.5 and became almost zero at x > 0.6. Judging from the very low Ms of Mg0.6Fe2.4O4 shown in Figure 3a, the corresponding broad peak from the (311) plane and disappearance of other peaks in Figure 4a seem to be due to scattering from para-crystal phase reflecting high disordered system. As shown in Figure 4d, the peak angles for ZnxFe3-xO4 decrased when x increased up to 0.4, and it was resulted from the broaden of crystal with the face-centered cubic inverse-spinal structure by the replacement of Fe3+ with Zn2+ in A-site up to 0.4. Beyond 0.4, the peak shifted inversely to high angles and the peak position at x = 0 is almost equal to that at x = 1.0. As discussed in the previous paper,1 this phenomenon is due to the fact that Zn doping gave the damage for the Fe3O4 crystal, since atomic size of Fe3+ (64 pm) is smaller than that of Zn2+ (74 pm). The ZnxFe3-xO4 crystal is less stable than the Fe3O4 one with increasing x. This indicated that x = 0.4 is attributed to the limit on forming the ZnxFe3-xO4 crystal. As described for the crystal size ( D ) and crystal unit number ( N ) of ZnxFe3-xO4 in the previous paper,1 D and N were: x = 0.1, 12.06 nm and 48, respectively; x = 0.2, 11.07 nm and 44, respectively; x = 0.3, 9.56 nm and 38, respectively; x = 0.4, at 7.59 nm and 30, respectively; x = 0.6, 7.84 nm and 31, respectively; x = 0.8, 11.08 nm and 44, respectively; and x = 1.0, 13.55 nm and 54, respectively. The length of a-axis in the cubic crystal unit cell was 0.8333 nm at x = 0, 0.8335 nm at x = 0.1, 0.8349 nm at x = 15 ACS Paragon Plus Environment


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0.2, 0.8353 nm at x = 0.3, 0.8389 nm at x = 0.4, 0.8384 nm at x = 0.6, 0.8352 nm at x = 0.8, and 0.8321 nm at x = 1.0, respectively. The length of the a-axis at x = 0.2 is longer than that at x = 0. Such information is very important, which shall be discussed later in Figure 15. That is, the expansion of crystal unit volume by Zn doping has advantage to prepare anodes of lithium ion batteries, since the large crystal unit volume accept a lot of lithium ion inside. The real profile of X-ray intensity distribution was obtained by convolution of the two intensity distributions measured for silicon particles and MgxFe3-xO4 at the indicated

x to pursue further detailed discussion about the crystal size. Figure 5a-c shows the corrected real X-ray diffraction curves (red curves) for MgxFe3-xO4 at the indicated x. Using the real curves (red curves), the crystal sizes (D311) obtained by the Scherrer’s equation are shown in Table 1. As discussed in previous paper,1 the calculation by the Scherrer’s equation is essentially insignificant, since the crystallite size of each particles is not constant and has the fluctuation. Hence the crystal unit cell of N was obtained as a distribution function by using the modified Laue function. This concept is somewhat complicated and then the evaluation procedure was described again briefly. By using somewhat modified Laue function, the diffraction intensity from perfect crystal with the crystal unit cell of N is given by

 2π  Nd sin θ  sin 2  λ  I (2θ ) = KC 2 π 2   sin 2  d sin θ  λ  


(1)

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where d is the lattice distance between the (311) planes listed in Table 1 and λ is the wave length of X-ray. K and C are constant and structural factor, respectively. However, it is of plausible to consider distribution of the number of crystal units within crystal domain, because the crystal domain of nanoparticles (MgxFe3-xO4) is much smaller than the irradiated X-ray beam area. The distribution of the crystal units number proportional to crystal size distribution is shown in eq(2) which follows by Gaussian distribution 1

 (N − N )2  exp −  2   2σ N P (N ) = 2N − 1  (N − N )2   ∑ exp− 2 N =1   2σ N

(2)

where N and σ N are the average number of crystal units and its standard deviation, respectively.40-41 The average diffraction intensity may be given by

I(2θ ) =

2N − 1

∑ P (N )I(2θ )

(3)

N =1

Based on the values of d and D311 listed in Table 1, the initial average number of

N . could be fitted by computer simulation. And in order to smear out the many subsidiary maxima on the both side of a main peak, the concept associated with eq 3 must be introduced.40 To give the same height of peak tops between experimental and calculated curves, eq 3 is normalized.



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Figure 5.

(a), (b) and (c) Experimental (red curve) and theoretical (black curve)

XRD intensity distribution functions of MgxFe3-xO4 for the indicated x. (d) Crystal diameter and crystal number distribution for Mg0.1Fe2.9O4. (e) TEM image of Mg0.1Fe2.9O4. (f) Domain size distribution for Mg0.1Fe2.9O4 by TEM image.

By choosing the optimal N and σ N , the calculated intensity distribution function (black curve) are in keeping with the experimental curves (red curve) as presented in Figure 5a~c. The listed values of N

and σ N were calculated by computer 18

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simulation. Incidentally, the values of N determined by Scherrer’s equation directly are slightly larger than the desirable ones values. The distribution P(N) against crystal unit number (upper side) and crystal size (lower side) is displayed in Figure 5d for MgxFe3-xO4 (x = 0, 0.1, 0.2). The average value ( D(= N × d) ) of size distribution could be obtained in relation to the peak top of

P(N) which was also shown in Table 1. The value of D tended to decrease with increase of Mg content, which was attributed to the destruction of Fe3O4 crystal by magnesium doping. In order to justify the calculated size distribution, TEM observation was performed in Figure 5e. The TEM observation for Mg0.1Fe2.9O4 specimen reveals that the particles exhibit a typical spherical shape as like Zn0.2Fe2.8O4.42 Further analysis for the domain size by the TEM results was performed and the size distribution of nanoparticles was shown in Figure 5f. The sizes are given in the range of 9~ 12 nm. These results keep well with average value of 9.87 nm which was calculated by X-ray. It indicates that each domain almost contained a uniform crystal structure of Mg0.2Fe2.8O4, different from agglomeration of the crystallites. Here it should be noted that the size by WAXD is slightly smaller than that by TEM and such phenomenon was also observed for Zn0.2Fe2.8O4.1, 18, 29 This was probably attributed to the existence of surface agent SDBS which stayed on the surface of the Mg0.2Fe2.8O4 nanoparticles to hinder the aggregation of the nanoparticles based on the report by Gnanaprakash et al. 43 To support the above concept, HR-TEM and SAED experiments are shown for (a) Fe3O4, (b) Mg0.6Fe2.4O4, and (c) Zn0.2Fe2.8O4 in Figure 6, in which the images on the left hand and the patterns on the right hand correspond to HR-TEM and SAED results,



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respectively. The HR-TEM images illustrate that the distance between adjacent lattice plane cannot be estimated exactly because of locally differences, but the scattered values were in the narrow range of 0.250 ~ 0.257 nm. Even so, the value is thought to be due to the d-spacing of the (311) plane of Fe3O4 from the results in Table 1. As for Fe3O4, the atom arranged orderly on the plane but the crystal lattice of Zn0.2Fe2.8O4 showed slight disordering by Zn doping. Obviously the lattice of Mg0.6Fe2.4O4 taken at twice scale showed considerable disordering in spite of the similar radius sizes of Mg2+ and Fe3+, indicating that the replacement of Fe3+ with Mg2+ in A-site and the decrease of the number of Fe2+ in B-site (see Figure 11a) caused drastic disruption of crystallites by the powerless super-exchange interaction between A- and B- sites and powerless double-exchange interaction in B-site, as discussed before. The rings in SAED became indistinct. Incidentally, it was confirmed that the HR-TEM image showed no lattice structure at MgxFe3-xO4 (x=1) and the corresponding SAED showed no diffraction ring. Accordingly, Figure 6 justifies the analyses for Figures 1~ 5 and Tables 1 ~ 3.


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Figure 6

HR-TEM images (left hand) and SAED patterns (right hand) : (a) Fe3O4, (b) Zn0.2Fe2.8O4, (c) Mg0.6Fe2.4O4.

To investigate the MgxFe3-xO4 structure whose domain size becomes smaller with increasing x, the dielectric property of MgxFe3-xO4 was investigated in comparison with ZnxFe3-xO4. The nanoparticles were molded as like films by compression. Figure 7a-b shows experimental results (open circles) for frequency dependence of the real (Z’) and imaginary parts (Z”) of impedance for the five nanoparticles, Fe3O4, Zn0.2Fe2.8O4, Mg0.1Fe2.9O4, Mg0.6Fe2.4O4 and MgFe2O4, respectively. Figure 7c-d shows the results (open circles) for frequency dependence of permittivity ( ε ' ) and electrical loss ( ε " ), respectively for the five specimens. The calculation for ε ' and ε " were carried out by 21 ACS Paragon Plus Environment


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(

(

using ε ' = (1 ωC0 ) − Z " Z '2 + Z "2

))

(

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(

))

and ε " = (1 ωC0 ) − Z ' Z '2 + Z "2 , respectively, in

which C0 is the geometric capacity given by ε 0 (S d ) , in which ε 0 is the vacuum permittivity (0.08854185 pF/cm), and S and d are the area of the molded nanoparticles like a film, which are represented in SI 1. The AC conductivity κ ( = ε " ε 0ω ) and

(

)

imaginary part of dielectric elastic modulus M" ( = ε " ε ' 2 +ε "2 ) are shown in Figure 7e-f, respectively. Figure 8 shows the Cole-Cole plots for Z* and complex electrical modulus M* for the five nanoparticles. Judging from the profiles of the ε ' and ε " in Figure 7c-d, the dielectric response modes for the five nanoparticles can be classified into two categories. The first one is the universal dielectric response (UDR) associated with power-law frequency dependence of AC conductivity reflecting high disordered system by heavy doping. Another one is the phase lags of crystalline nanoparticle (grain) resistance and grain boundary in addition to the phase lag of resistance between the nanoparticles and two electrodes. The former is the characteristics of plateau-like (dull) decrease of ε ' at low frequency and of appearance of a broad peak curve of ε " at high frequency corresponding to starting of the drastic decrease of ε ' . This tendency is observed for Mg0.6Fe2.4O4 and MgFe2O4.

Such frequency dependences of ε ' and ε " have been

reported for all doped or dirty semiconductors.44-46 Actually by a large amount of magnetic doping, very small Mg0.6Fe2.4O4 formed very small crystal with lattice disordering and MgFe2O4 particles could not form crystal as shown in Figure 4a and Figure 6.


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Figure 7.

Frequency dependence of Z’, Z”, ε ' , ε " , κ and M” for the indicated

specimens. The experimental and calculated results are represented as different color open circles and the color curves, respectively. The calculated results of Mg0.6Fe2.4O4 and MgFe2O4 are obtained by fitting of parameters in eqs 4 and 5 and those of Fe3O4, Mg0.1Fe2.9O4 and Zn0.2Fe2.8O4 by fitting of parameters in eq 6.



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Figure 8.

Cole-Cole plots of Z* and M* for Mg0.6Fe2.4O4, MgFe2O4, Fe3O4,

Mg0.1Fe2.9O4 and Zn0.2Fe2.8O4. The experimental results (open circle) and calculated results (red curve).

The UDR is the most common approach to take into account the hopping conductivity of localized charge carrier. Considering the intrinsic contribution about highly disordered particles and extrinsic contribution between the nanoparticles and two 24 ACS Paragon Plus Environment

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electrodes, frequency dependence of ε ' and ε " are given by using the power law of

ε " and Kramers-Kronig relation,47 as represented by eqs 4 and 5. This is based on model A in Figure 9

ε '= ε∞ +

ε"=

σ0 ∆ε  nπ  n −1 tan ω + ε0 1 + ω 2τ 2  2 

σ 0 n −1 σ 0 ∆εωτ ω + + ε0 ωτ 1 + ω 2τ 2

(4)

(5)

where ω = 2πf is angular frequency and σ 0ω n is the UDR used for frequency dependence AC conductivity, σ 0 is the DC conductivity, τ is the relaxation time and

n is an exponential factor from 0.5 to 0.7. ∆ε is given by ε 0 − ε ∞ , in which ε ∞ is the high frequency value of ε ' and ε 0 is the dielectric constant of contact region.

Figure 9.

Model A used to explain eqs 4 and 5, Model B to explain eq 6 and Model C proposed to explain Model B.



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As shown in Figure 8, the theoretical calculation results for ε ' and ε " (color curves) provide good fitting with the experimental ones with plateau-like decrease of

ε ' at low frequency and a very broad peak of ε " at high frequency, which justified the UDR. The parameters to give the best fittings are listed in Table 2. Among the parameters, the most important parameter n (0.5 ~ 0.7) characterizing UDR was 0.550 for MgFe2O4 and 0.635 for Mg0.6Fe2.4O4 indicating that MgFe2O4 is a highly disordered system. This result is in good agreement with the WAXD intensity distribution in Figure 4a.

Table 2.

Parameter fitting values for Mg0.6Fe2.4O4 and MgFe2O4

Parameters

Mg0.6Fe2.4O4

MgFe2O4

ε∞

10.8

60.0

N

0.635

0.550

σ0

9.00 × 10-10

1.14 × 10-8

∆ε

1400

30000

Τ

1.00 × 10-5

3.20 × 10-5

By using the parameters listed in Table 2, the frequency dependence of Z’ and Z” in addition to M” as well as Cole-Cole plots for Z* and M* were calculated by the parameters for Mg0.6Fe2.4O4 and MgFe2.0O4, which is shown in Figure 7. Of course, good fitting between experimental and calculation results could be obtained. Based on the results, Cole-Cole plots for Z* and M* are shown in Figure 8a-b for Mg0.6Fe2.4O4 and Figure 8c-d for MgFe2O4. Of course, the Cole-Cole plots showed increasing curve of Z” (M”) with increasing Z’ (M’) without forming circular arc reflecting typical profile of UDR behavior. 26 ACS Paragon Plus Environment

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In contrast, as shown in Figure 7c-d already, ε ' and ε " for Fe3O4, Zn0.2Fe2.8O4 and Mg0.1Fe2.9O4 show the resemble behaviors different from MgFeO4 and Mg0.6Fe2.4O4, since the three specimens have crystal domains > 9.8 nm showing clear X-ray diffraction peaks (see Figure 4a). The dielectric properties of the three crystalline nanoparticles are different from UDR behavior which have been observed for nanoparticles with a highly disordered system. Furthermore, the frequency dependence of Z” in Figure 7 and the Cole-Cole plots of Z* in Figure 8e, 8g, 8i and M* in Figure 8f, 8h, 8j indicate phase lags of resistances more than two modes. To determine the model system, first of all, peak separation of the composites of Z* in Figure 7a-b was carried out by computer for the three specimens, since the profiles could not be realized by UDR. Figure 10 shows the results represented as logarithmic scale. Through trials and errors, the summation of three circuits calculated on the basis of Model B in Figure 9 is in good agreement with the experimental result (open circle) for the three nanoparticles. Model B shows three connected arrangement of normal parallel circuit with resistance and capacitance and two parallel circuits with resistance and constant phase elements (CPE).

48-50

The concept of CPE has been introduced to

replace the ideal capacitor of the Debye model based on a number of findings those the measured impedance loci in the complex plain were in the form of circular arcs with depressed circular center. The parameters also provide the good fitting about frequency dependence of ε * as well as the complex electrical modulus M* and the Cole-Cole plots of Z* and M*. The outline of the concept is represented as Model C in Figure 9. The parameters to give the best fittings were obtained by computer simulation using eq 6 which was formulated on the basis of Model B. The parameter values are listed in Table 3. 27 ACS Paragon Plus Environment


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Z* =

Figure 10.

1 1 1 + + 1 1 1 α β + iωC1 + (iω ) C2 + (iω ) C3 R1 R2 R3

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(6)

The individual Z’ and Z” components of the first, second and third circuits

for Fe3O4, Mg0.1Fe2.9O4 and Zn0.2Fe2.8O4 calculated by eq 6 using Model B in Figure 9 and the each summation was shown in a red line.

The first component (ultramarine curve) of Z” in Figure 10 provided a peak at low frequency indicating extrinsic resistance between nanoparticles (grain) surface and 28 ACS Paragon Plus Environment

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electrode, the second component (blue curve) provided a peak at middle frequency indicating intrinsic contribution of grain boundary resistance, and the third component (green curve) provided a peak at high frequency indicating nanoparticle resistance. The first component may reveal a normal circuit with resistance and capacitance associated with Debye relaxation. Since the exponent is unity (see Table 3), the surface of the molded ferrites was smooth. In contrast, α = 0.6449 at the second component indicated roughness of grain boundary surface. Anyway, the total of the three components of Z” are in good agreement with the experimental results. Good agreement was also realized for the frequency dependence of Z’ for the three ferrite films as shown in Figure 10a, 10c and 10e. And the corresponding Z” values also showed good agreement in Figure 10b, 10d and 10f.

Table 3.

Parameters in Model B in Figure 9 to give the best fitting between experimental and theoretical results. Fe3O4

Mg0.1Fe2.9O4

Zn0.2Fe2.8O4

Model type

B

B

B

R1 (Ω)

1.818×105

3.798×105

5.101×104

C1 (pF)

1.505×102

1.315×103

1.303×102

R2 (Ω)

1.597×106

3.211×106

6.582×105

C2 (pF)

1.007×106

1.757×105

6.926×105

Α

0.3951

0.5932

0.6449

R3 (Ω)

1.109×106

2.501×106

2.826×105

C3 (pF)

5.063×103

2.354×101

1.168×103

Β

0.6551

0.9021

0.8341



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Returning to Figure 8 and Table 3, the characteristic behavior was observed for the frequency dependence of ε " and κ . The ε " decreased linearly for the molded three ferrite nanoparticle films (Fe3O4, Zn0.2Fe2.8O4, Mg0.1Fe2.9O4) indicating predominant of DC component and the corresponding κ revealed gradual increase up to 103 Hz and steep increase beyond 103 Hz. Different from Mg0.6Fe2.4O4 and MgFe2O4 with high disordered system, M” for the three ferrites revealed a broad peak but the each profile is quite different from Debye relaxation because of the exponent α = 0.6449 for the grain boundary resistance and α = 0.8341 for nanoparticle (grain) associated with patterned indented surface. Such behavior has been observed normally for conductive filler and polymer composites.48-50 Based on the knowledge discussed above, the Cole-Cole plots of Z* and M* for the molded three ferrite films in Figure 8 were analyzed in detail. The peak top of Z* appeared in the range 630.96 ~ 6309.6 Hz is attributed to the grain boundary resistance and the peak at 25.1 Hz appeared for Zn0.2Fe2.8O4 is attributed to resistance between the nanoparticle film and electrode. On the other hand, the peak of the suppressed circular arc of M* appeared beyond 10000 Hz is obviously attributed to the resistance for charge movement within nanoparticle grains (particles). Interestingly, the dielectric properties of the three ferrites represented by the threecircuit model (Model B in Figure 9) are important to ensure high capacitance and the stability as anode of lithium ion batteries, which shall be discussed in Figure 15 later. As a well-known fact, the number of Fe3+ ions in tetrahedral space (A-site) and octahedral space (B-site) is the same, in which the Fe3+ ions in A- and B-sites are surrounded by four and six oxygen ions, respectively. In B-site, the number of Fe3+ ions is equivalent to that of Fe2+ ions.26,

51

However, it is difficult to distinguish the 30

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difference between Fe3+ and Fe2+ ions and the spin directions in Fe3+ and Fe2+ ions. This is attributed to electron hopping between adjacent Fe3+ and Fe2+ ions through hybrid orbital formed with 2p orbital of oxygen ion resulted from the double-exchange interaction. When Fex3+ ions in A-site are replaced with Mg2+ ions, the same number of Fe2+ ions in

B-site

[Mg

2+ x

Fe1− x

changes 3+

] [Fe A

3+

to 3+

Fe x Fe1− x

Fe3+ 2+

]O B

ions 4

by

electron

emission

and

form

. In this process, the spin direction of the resulting

Fex3+ ions in B-site influences the magnetization of Mg doped Fe3O4 as shown in Figure 3. In order to show the mechanism vividly, a diagrammatic sketch for the substitute of Fe3+ with Mg2+ in A-site is shown in Figure 11 based on the Hund’s rule. In the diagram, there were 10 Fe3+ ions in A-site and 10 Fe3+ and 10 Fe2+ ions in B-site for Fe3O4 (at x = 0) and the vanishing of Fe3+ ions in A-site with increase of x reveals the substitute with Mg2+ ions. Due to the super-exchange transition between Fe3+ in A-site and Fe3+ in B-site , the magnetic moment for Fe3O4 (at x = 0) was offset perfectly and the effective magnetic moment was only endowed by Fe2+. For the MgxFe3-xO4 nanoparticles, Mg2+ ions would replace the Fe3+ ions in A-site. When x = 0.1, Mg0.1Fe2.9O4, one Fex3+ ion was replaced and one Fe2+ ion in B-site changes to Fe3+ ion to keep electric neutrality of the crystal unit, which is associated with double-exchange interaction resulting in electron hoping in B-site. At x = 0.2, however, the spin directions of one Fex3+ ion among two Fex3+ ions were anti-parallel to decrease the magnetization, meaning occurrence of super-exchange interaction between original Fe3+ and Fe3+ produced by one electron emission of the original Fex2+ ion in B-site.



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Such a proposal is a new idea, since the super-exchange reaction has been established between Fe3+ ion in A-site and Fe3+ ion in B-site through hybrid orbital formed with 2p orbital of oxygen ion. However, the generation of Fe3+ ion with anti-parallel spin in B-site can not be explained by the usual concept. Hence at x = 0.2, the magnetization associated with two resultant Fe3+ ions in B-site becomes almost zero and the total magnetization of Fe3+ in B-site at x = 0.2 may be equal to that at x = 0. At x higher than 0.2, the super-exchange interaction in B-site through hybrid orbital formed with 2p orbital of oxygen ion is superior to double-exchange one. The experimental results in Figure 3a-b support this concept. If this is the case, the further magnesium doping beyond 0.3 is difficult because of predominant of the super-exchange interaction of Fe3+ ion in B-site. Actually, in the present experiment, Ms became lower with increasing x and it was impossible to form crystals at x = 0.6. Actually, the measurement of Ms was impossible at x > 0.6. Figure 11a shows that at x = 0.6, the number of Fe3+ ions with anti-parallel direction ( ↓ ) become five and that of Fe2+ ions with parallel direction ( ↑ ) was four in B-site, while the number of Fe3+ ions with anti-parallel direction ( ↓ ) in A-site was four. Such a structure provides a presumption that an increase in resultant Fe3+ ions with direction ( ↓ ) by one electron emission of Fe2+ ion constrict to cause the double-exchange interaction in B-site while the number of Fe3+ ions in A-site is too few to maintain crystal unit at x = 0.6. Actually, as shown in Figure 4a, the crystal peak disappeared perfectly at x > 0.6.


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Figure 11.

(a) Schematic diagram by replacement of Fe3+ ion with Mg2+ ions for x = 0

~ 0.6 in A-site. (b) Calculated M/Ms(0) based on model (a). Ms(0) is the value of M at 9000 Oe for x = 0.

Here it should be noted that the behavior of Ms for MgxFe3-xO4 is different from that for ZnxFe3-xO4 reported in the previous paper.1 The Ms for ZnxFe3-xO4 became maximum at x = 0.2. This indicates two Fe3+ ions are replaced with two Zn2+ ions in the A-site and two Fe2+ ions in the B-site change to Fe3+ ions by one electron emission instantaneously to keep electric neutrality. In this case, the same spin direction was maintained. This is due to the fact that, in the case of Zn doping, the double-exchange interaction caused the electron hopping between adjacent original Fe3+ ion and the Fe3+ ion resulted from Fe2+ 33 ACS Paragon Plus Environment


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ion by one electron emission (to keep electron neutrality) in B-site is ensured at x = 0.2. At x = 0.3, however, the electron transfer is similar to that of MgxFe3-xO4 (x > 0.1). Based on the above idea creation, theoretical estimation for the magnetization was performed as a function of the applied magnetic field by using Brillouin function as reported in the previous paper1, in which the angular quantum number L could be neglected and total angular moment J is postulated to be equal to the total spin number S of d orbital. The average magnetic moment

µJ

under magnetic field H at absolute

temperature T is given as follows: µJ

 2J + 1  2J + coth  = Jgµ B  J 2  2J 

 Jgµ B H 1  Jg µ B H  1  coth  − kT J 2   2JkT 

  Jg µ B H   = Jg µ B B J     kT

 (7)  

where g denoting g-factor for spin is given by 2.0023 assuming free electron, µ B is Bohr magneton, and k is Boltzmann constant. Considering L = 0, J for Fe 2+ is given by J1 = 2, while J for Fe 3+ is given by J2 = 5/2. Judging from Figure 11, the average magnetic moment of MgxFe3-xO4 is given as follows:

µ(x ) 2gµ B

=

M (x ) = (1 − x ) µ J Ms(0)

=

M (x ) = (1 − x ) µ J Ms(0)

1

+ 2x µ J 2

1

+ 0.1 µ J 2

x ≤ 0.1

(8)

and

µ(x ) 2gµ B

0.1 < x ≤ 0.6

Eq 7 is normalized by Ms(0) (Ms at x = 0) to carry out the numerical calculation.


(9)

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Figure 11b presents M/Ms(0) results estimated against H at 25oC. The results were compared with the experimental results (as shown in Figure 3b). At x = 0, 0.1, 0.2, the calculated profile slightly provides good agreement with the experimental one, but the calculated profiles deviate from the experimental ones with increasing x, which is due to the fact that eq 7 is formulated without considering the two factors, the drastic decrease of crystal size with increasing x as listed in Table 1 and the domain (particle) size distribution of the particles is presented in Figure 5. Actually, at x = 0.6, the normalized theoretical Ms is 0.49, which is much higher than the experimental value 0.17 (see Figure 3b). As a final goal, the nanostructured Fe3O4/MWCNT, Mg0.1Fe2.9O4/MWCNT and Zn0.2Fe2.8O4/MWCNT composites were evaluated as anodes for lithium ion batteries. Of course, as preliminary experiments, the damage of MWCNTs by heat treatment associated with the preparation of the composites was investigated by WAXD and Raman spectroscopy. No change of WAXD peak and profile from the (002) plane was confirmed by eqs 1 and 3. In Raman spectrum shown in SI 2 (Figure S1) , however, the slight decrease of G-band was confirmed in comparison with D-band. As the results, the damage of MWCNTs was found to be hardly affected by the heat-treatment. Of course, the ferrite crystal unit sizes perfectly were not affected. Figure 12 shows three TEM images for the formation of ferrites, (a) Fe3O4, (b) Mg0.6Fe2.4O4, and (c) Zn0.2Fe2.8O4 along acid treated MWCNTs. The ferrites are thought to be combined on the external surface of chemically modified MWCNTs with many functional groups such as OH, COOH, C=O. As discussed elsewhere,

6, 52-53

these

groups of the purified MWCNTs easily interact with functional groups on PVA chains to form hydrogen bonds in the interface of MWCNTs. The PVA could help MWCNTs 35 ACS Paragon Plus Environment


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weltering the aquatic phase and enhance the stability of their dispersion. The PVA had bifunctional bridges with hydrophilic groups jointed with the ferrite nanoparticles, and hydrophobic chains adhered to the MWVNT surfaces. Hence the nanostructured ferrites were deposited on the external MWCNT surfaces through PVA. When the as-prepared samples were calcined at 500 oC, the PVA melted and coated on the external MWCNT surfaces to prevent separation of ferrite particles from the MWCNTs’ external surface. Such process is shown as schematic diagram in Figure 1.

Figure 12.

TEM images of ferrite-MWCNT composites (a) Fe3O4/MWCNT, (b) Mg0.6 Fe2.4O4/MWCNT, (c) Zn0.2Fe2.8O4/MWCNT.

Due to the nanosize of Fe3O4 and CNTs and their dark color, it is difficult to recognize the Fe3O4 from the TEM observation directly. Thus, WAXD measurements were carried out to prove that Fe3O4 and CNTs exist in the physical mixing composite and the composite annealed for Fe3O4, MWCNT, and PVA, which was shown in Figure 13. In the diffraction curve (red) from composite by physical mixing, a strong diffraction peak from (002) plane (2θ=26.7°) associated with the MWCNT was observed, in addition to the very clear peaks from the (220), (311), (400), (422), (511) and (440) planes for Fe3O4. On the other hand, the diffraction curve (black) of the composite produced after annealing the physical mixture of Fe3O4, MWCNT and PVA 36 ACS Paragon Plus Environment

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shows that all the peak profiles from the Fe3O4 were almost the same as those of the curve (red) but only the (002) peak was broader. This result proved the adhesion of ferrite nanoparticles on MWCNTs together with carbonized PVA in the annealed composites clearly.7 The broad peak is probably due to overlapping of the diffraction of carbonized PVA and the disruption of MWCNT by annealing. In the preliminary paper 53

, it was reported that PVA carbon film provides a broad peak at ca. 2θ=26.7°.

Accordingly, it is obvious that the carbonized PVA stay in the annealed composites.

Figure 13. Two X-ray diffraction intensity curves; curve (red) from physical mixture of Fe3O4 and CNTs curve (black) from annealed Fe3O4 /CNTs composites.

Figure 14 shows schematic diagrams of the present experiment different from the commercial lithium ion batteries. The present experiment system was adopted to simplify the evaluation for electrochemical performance of the ferrite/MWCNT nanocomposite. Hence the ferrite/MWCNT composite was set as cathode and the lithium metal was set as anode. Of course, the inverse setting different from commercial lithium battery is the usual way in the laboratory level.



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Figure 14.

Schematic diagram adopted in the present experiment to evaluate

electrochemical performance of the ferrite nanocomposite.

Incidentally, in preliminary experiment, the weight-corrected magnetizations against applied magnetic field for

the

Fe3O4/MWCNT, Mg0.6Fe2.4O4/MWCNT, and

Zn0.2Fe2.8O4/MWCNT composites were confirmed to be almost equal to those of Fe3O4, Mg0.6Fe2.4O4, and Zn0.2Fe2.8O4 shown in Figure 3. The purpose of the experiment is the further improvement of cyclic performance of Fe3O4/MWCNT composite, although it was reported that Fe3O4 electrode has the higher theoretical reversible capacity (926 mAhg-1) when discharging to 0 V versus lithium metal due to one Fe3O4 can react with about eight lithium ions.3 The selection of Zn0.2Fe2.8O4/MWCNT composite is due to the fact that Zn0.2Fe2.8O4 is larger volume crystal unit in comparison with Fe3O4 and has the possibility to accept more lithium ions in the crystal unit, since each gap between vicinal atoms in the crystal unit becomes longer. Figure 15a shows the capacitance of the molded ferrite films against cycle number under discharge and charge. The capacitances under charge and discharge were almost the same indicating good cycle performance. That is, the capacitance for the three 38 ACS Paragon Plus Environment

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ferrites decreased drastically with increasing the cycle number. The capacitance of Zn0.2Fe2.8O4 becomes higher than that of Fe3O4 in the cycle number from the third to tenth. The capacitance of Mg0.6Fe2.4O4 was the lowest up to seventh but the value became almost equal to those of Zn0.2Fe2.8O4 and Fe3O4 beyond seventh. As shown in Figure 15b, however, capacitances of ferrite/MWCNT composites are stable under discharge and charge. The capacitances of the first discharge for Zn0.2Fe2.8O4

and

Fe3O4

Zn0.2Fe2.8O4/MWCNT

are

composite

very

large.

provided

Among the

the

highest

three

composites,

capacitance

and

Mg0.6Fe2.4O4/MWCNT composite was the lowest. As can be seen WAXD curves in Figures 4a and frequency dependence of ε * and ε " in Figure 7, WAXD curve (Figure 4a) showed a very weak diffraction peak from the (311) plane and ε ' in Figure 7c and

ε " in Figure 7d shows the typical frequency dependence of UDR associated with power-law frequency dependence of AC conductivity for amorphous substances for Mg0.6Fe2.4O4. This indicates that amorphous nanoparticles are useless as electrode of lithium ion batteries and capacity of Mg0.6Fe2.4O4/MWCNT against cycle number under discharge and charge reflects only the capacitance contribution of MWCNTs. In contrast, the Fe3O4/MWCNT and Zn0.2Fe2.8O4/MWCNT composites provided the high and reversible capacitance against the cycle number under discharge and charge. The Zn0.2Fe2.8O4/MWCNT is better than the Fe3O4/MWCNT as electrode of lithium ion batteries. Judging from a longer length of the a-axis of cubic crystal unit of Zn0.2Fe2.8O4 in comparison with that of Fe3O4, the crystal unit volume of Zn0.2Fe2.8O4 is bigger and the each space between vicinal atoms in the crystal unit is slightly bigger. Hence it may be postulated that Zn0.2Fe2.8O4 crystal unit can accept more lithium ions than Fe3O4 crystal unit. Even so, the capacitance of the present Zn0.2Fe2.8O4/MWCNT composite is 39 ACS Paragon Plus Environment


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lower than the result for Fe3O4/MWCNT reported in the previous paper.7 This reason is attributed to small amount of Zn0.2Fe2.8O4 nanoparticle content (24.6%) much lower than 66.7% of Fe3O4 reported already.7 When the same content (66.7%) of Zn0.2Fe2.8O4 is combined along MWCNT, the capacitance of Zn0.2Fe2.8O4/MWCNT composite is expected to be better than that of Fe3O4/MWCNT composite. Incidentally, in so far as the results of the real part of the complex permittivity and the conductivity ( κ ) at 1 Hz in Figure 7, the DC component of dielectric property is thought to be independent of capacitance of lithium ion batteries. Interestingly, the capacities of the three ferrite films were almost the same beyond 10 cycles. This is probably thought to be due to the fact that lithium ions entered in the crystal units could not contribute to the charge and discharge beyond 10 cycles without existing MWCNTs. The charge and discharge of lithium ions for ferrite crystal units of Zn0.2Fe2.8O4 and Fe3O4 are thought to be similar to those for MWCNTs and then the expansion of the Zn0.2Fe2.8O4 crystal unit by zinc doping causes the significant effect on the charge and discharge of lithium ions. However, the charge and discharge are ineffective in the disordered system such as Mg0.6Fe2.4O4/MWCNT. The capacitances under discharge and charge are stable up to 80 cycles as shown in Figure

15c.

The

columbic

efficiency

represented

as

ratio

of

charge

capacitance/discharge capacitance discharge is beyond 95% beyond fifteenth cycle indicating very stable reversible electric devices. However, the large capacity difference was found for the three ferrite/MWCNT composites as shown in Figure 15b. This reason remains unresolved problem.


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A series of experimental and theoretical analyses reveals that detailed fundamental investigation for nanocomposite characteristics plays an important role to develop high quality devices.

Figure 15.

(a) Cyclic performance of Fe3O4, Zn0.2Fe2.8O4, Mg0.6Fe2.4O4. (b) Cyclic

performance of Fe3O4/MWCNT, Zn0.2Fe2.8O4/MWCNT, Mg0.6Fe2.4O4/MWCNT composites. (c) Coulombic efficiency of Fe3O4/MWCNT, Zn0.2Fe2.8O4/MWCNT, Mg0.6Fe2.4O4/MWCNT composites.

CONCLUSION Mg

doped

Fe3O4

nanoparticles,

MgxFe3-xO4,

provided

slightly

better

super-paramagnetism at x = 0.1 than original Fe3O4 but the saturated magnetization Ms decreased with increasing x beyond 0.2. When one Fex3+ ion is replaced with Mg2+ ion



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in A-site (Mg0.1Fe2.9O4), one Fe2+ ion in B-site changes to Fe3+ ion with keeping the same spin direction by emission of one electron in order to maintain electric neutrality of the crystal unit. For Mg0.2Fe2.8O4 (x = 0.2), however, the spin direction of one Fex3+ ion among two Fex3+ ions must be anti-parallel to cause the decrease of the magnetization, which indicates occurrence of super-exchange interaction between resulting Fe3+ and Fe3+ produced by one electron emission of the original Fex2+ ions in B-site. The super-exchange interaction is postulated to be more effective than double-exchange one at x higher than 0.2. The volume of crystal unit was constant in spite of an increase in x, since radius (65 pm) of Mg2+ ion incorporated in A-site is almost equal to the radius (64 pm) of replaced Fe3+ ion. However, the crystal size also decreased. At x = 0.6, WAXD intensity curve showed no diffraction peak indicating that Mg0.6Fe2.4O4 became high disordered nanoparticle and the dielectric property showed the typical frequency dependence of UDR associated with power-law frequency dependence of AC conductivity for amorphous substances. On the other hand, Zn doping

Fe3O4

nanoparticles,

ZnxFe3-xO4,

provided

the

most

predominant

super-paramagnetism at x = 0.2 but Ms becomes lower beyond 0.4 in comparison with Ms of Fe3O4. The doping Zn2+ radius (74 pm) in A-site was bigger than the radius (64 pm) of replaced Fe3+ ion and then the crystal unit volume becomes bigger with increasing x. However, the crystal unit volume tended to decrease with increasing beyond x = 0.4 indicating that the Fe3O4 nanoparticles did not accept more doping of Zn2+. The imaginary part of complex impedance classified into three type phase lags of resistances associated with nanoparticle (grain), grain boundary and interface between grains and anodes as has been reported for ceramics.


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Based on the knowledge, electrochemical performance of nano-structured ferrite/MWCNT composites were evaluated in terms of the volume of the ferrite crystal unit. Of course, the high and reversible capacity against cycle number under discharge and charge coulombic efficiency was ensured because of the existence of MWCNTs. For Mg0.6Fe2.4O4/MWCNT composite with amorphous fine powder of Mg0.6Fe2.4O4, the capacity under discharge and charge was the lowest, while the capacity of Zn0.2Fe2.8O4/MWCNT composite was the highest, since the crystal unit volume of Zn0.2Fe2.8O4 with the longest length of the a-axis is the biggest. Hence it may be postulated that the space in the Zn0.2Fe2.8O4 crystal unit is slightly wider than that in Fe3O4 crystal unit and then Zn0.2Fe2.8O4 crystal unit can accept more lithium ions than Fe3O4 crystal unit.

ASSOCIATED CONTENT Supporting Information The sample’s dimension information for the dielectric measurement and the Raman spectra results of ferrite-MWCNT nanocomposites were described in the Supporting Information. This information is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email address: [email protected] (M. M.) Tel/Fax: +86 411 84986093

Notes 43 ACS Paragon Plus Environment


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The authors declare no competing ﬁnancial interest.

ACKNOWLEDGEMENT The authors acknowledge the financial support from the National Natural Science Foundation of China (NSFC) programs (No. 21374014). The authors thank to Prof. Tashiro and his student, Department of Future Industry-oriented Basic Science and Materials, Graduate School of Engineering, Toyota Technological Institute of Japan, to take TEM images shown in Figures 5e and Figure 12.

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TOC GRAPHIC

Magnetic Behaviors of Mg and Zn doped Fe3O4 Nanoparticles Estimated in Terms of Crystal Domain Size, Universal Dielectric Response and Application of Fe3O4/CNTs Composites to Anodes for Lithium Ion Batteries Zhongyuan Lv,1) Qi Wang,2) Yuezhen Bin,1, 3) Ling Huang,2) Rong Zhang,4) Panpan Zhang, 1) and Masaru Matsuo*1, 3)


Magnetic Behaviors of Mg- and Zn-Doped Fe3O4 Nanoparticles

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