Effect of Size on the Structural Transition and Magnetic Properties of

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Effect of Sizes on Structural transition and Magnetic Property of Nano-CuFe2O4 Wenjuan Zhang, Yongqiang Xue, and Zixiang Cui Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03468 • Publication Date (Web): 25 Oct 2017 Downloaded from http://pubs.acs.org on October 28, 2017

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Industrial & Engineering Chemistry Research

Effect of Sizes on Structural transition and Magnetic Property of Nano-CuFe2O4 Wenjuan Zhang, Yongqiang Xue*, Zixiang Cui Department of Applied Chemistry, Taiyuan University of Technology, Taiyuan 030024, China *Corresponding author: [email protected]

ABSTRACT Advances in the fields of chemistry often involve nanoparticles, which structural transition surprisingly different from the bulk material, and the difference between them is mainly attributed to the size of nanoparticles. In this paper, tetragonal nano-CuFe2O4 (t-CuFe2O4) with different sizes ranging from 32 to 79 nm was prepared using high temperature solid phase method. The structural transition of nano-CuFe2O4 from tetragonal to cubic was determined by differential scanning calorimetry (DSC). The theoretical derivations and experimental tests indicate that, as the decrease of size, the temperature, the enthalpy and the entropy of structural transition of nano-CuFe2O4 decrease accordingly and present linear variation with the reciprocal of sizes, respectively. Furthermore, the effect of particle sizes on magnetic property of nano-CuFe2O4 was investigated. The results show that size of of nano-CuFe2O4 can obvious effect the magnetic properties: with the particle size of nano-CuFe2O4 decreases, the saturated magnetic induction decreases, the coercivity increases, while the remanence decreases.

Keywords：Nano-CuFe2O4; Structural transitions; Size dependence; Magnetic properties

1. Introduction The different structures of nanoparticle can exhibit special physical and chemical properties. For example, the rutile structure of TiO2 is used for electronic products because of its high dielectric constant,1 and the anatase for catalysts,2 while the mixed-structure typically displays higher photoactivity than the pure phase.3 Not only that, the structural transition of nanoparticles plays a key role during the significant process of chemistry. As in functional ceramics field, the

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structural transition of nanoparticles is used to enhance multiferroic and toughness of ceramic materials.4,5 Indeed despite extensive studies into structural transition,6-13 little attention has been devoted to the quantitative correlations between integral enthalpy, integral entropy and sizes of nanoparticles. Hence, it is significant in science and practice to research and ascertain the effects of size of nanoparticles on thermodynamics of structural transition. Previous researches have shown the effects of size of nanoparticles on thermodynamics of structural transition. Tveryanovich et al.14 obtained the nano-AgI with the thickness of the layers ranging from 10 to 100 nm using laser ablation, studied the structural transition of β to α by Rigaku Ultima IV X-ray diffractometer and they found that, with the decreasing size of nanoparticle, the temperature of structural transition corresponding decreases. Xiao et al.15 performed a DSC test to investigate the structural transition of BaTiO3 of different grain sizes, the test results show that the structural transition enthalpy reduced with decreasing grain size. Jiang et al.16 proposed an improved phenomenological theory by taking the size effects on phenomenological coefficients into account. Both the experimental results and theoretical calculation illustrate that the entropy jump of nano-PbTiO3 decreases as the decreasing size of nanoparticles. Among these nanoparticles of structural transition, nano-CuFe2O4 has been used widely in variety of areas of production, such as magnetic material17, electrode material18, catalyst19, dielectric material20 and so on, due to its attractive magnetic, electronic, thermal and catalytic properties. In this account, we take the structural transitions of nano-CuFe2O4 from tetragonal to cubic as a research subject, the influence regularities of size of nano-CuFe2O4 on the temperature, the integral enthalpy and entropy of structural transition were discussed, respectively. Furthermore, the effect of particle sizes on magnetic property of nano-CuFe2O4 was studied.

2. Theoretical In the structural transition process of spherical nanoparticles from α phase into β phase, the change in the molar Gibbs energy ( ∆ α Gm ) is, β


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∆ βα Gm = Gmβ − Gmα = ∆ βα Gmb −

3Vασ α 3Vβσ β + rα rβ

(1)

where Gmα , σ α , Vα and rα are the molar Gibbs energies, the surface tension, the molar volume and the radius and of α phase, respectively; Gmβ , σ β , Vβ , and rβ are that of corrosponding physical quantities of β phase, respectively; Superscript b denotes the properties for the bulk substance, ∆ βα G mb = ∆ G mb (β) − ∆ Gmb (α) . In addition, the mass remains unchanged before and after phase transition, so for spherical nanoparticles,

4 3 4 4 π rα ρα + π ( rβ3 − rα3 ) ρβ = π r 3 ρα 3 3 3 where

(2)

ρ denotes densities.

That is to say,

ρ = α rα  ρ β rβ

1

1

 3  Vβ  3  =    Vα  

(3)

Hence,

 ρβ  3Vασ α 3Vβσ β 3Vα  − = σ α − σ β   rα rβ rα   ρα  3Vβ  ∂ σ β  3Vα  ∂ σ α  3Vα   =   − rα  ∂ T  P rβ  ∂ T  P rα

2   3 ∂ σ ρ     ∂ σ   β β  α  −   ∂ T  P  ∂ T   ρ α   P  

(4)

(5)

For a general substance, ρα ≈ ρ β , Eq. (4) and (5) can be approximated as,

3Vασ α 3Vβσ β 3Vα − = (σ α − σ β ) rα rβ rα 3Vβ  ∂σ β  3Vα  ∂σ α  3Vα  ∂σ α   ∂σ β   − −    =     rα  ∂T  P rβ  ∂T  P rα  ∂T  P  ∂T  P 

(6)

(7)

The Eq. (8) can be derived as follow after the application of Gibbs-Helmholtz equation to the process of structural transition,

 ∂  ∆βαGm   ∆βα H m    = − T2  ∂T  T   p


(8)


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where ∆ βα H m represents the molar enthalpy of phase transition. Inserting Eq. (1) into Eq. (8), our group has,

∆βαHm = ∆βα Hmb (Tb ) −

+

3Vα   ∂σα  2Tbσααα  σα −Tb   −  rα  3   ∂T P

3Vβ   ∂σ β  2Tbσ βα β  Tf σ β − Tb   + C p ,β (T ) dT  − 3  ∫Tb rβ   ∂T  P

where Tb and Tf are the initial and final melting temperatures, respectively;

(9)

α α and α β are

the volumetric expansion coefficient of the α phase and the β phase, respectively. C p ,β is the isobaric molar heat capacity of β phase. Basing on the essential thermodynamic relation, the molar entropy ( ∆ α S m )of structural β

transition can be written as,

 ∂∆β G  ∆βα Sm = −  α m   ∂T  p

(10)

∆ βα S m can be expressed as follow by inserting Eq. (9) into Eq. (10),

∆βα Sm = ∆βα Smb (Tb ) +

−

3Vα rα

 ∂σ α  2σ αα α    +  3   ∂T  P

3Vβ  ∂σ β  2σ βα β  Tf C p ,β (T ) dT  +  + rβ  ∂T  P 3  ∫Tb T

(11)

For general nanoparticles, the orders of（ ∂σ / ∂T）p , T, α, Vm , σ are 10-4 J·m-2·K-1,21 102 K, 10-5,22,23 10-5 m3·mol-1 and 10-1∼100 J·m-2,24 respectively, and （∂σ / ∂T）p < 0 . So the ∆ βα H m and the ∆ βα S m are mainly determined by Eq. (6) and Eq. (7), respectively. If σ α > σ β , it is shown that β phase is stable compared to α phase, and there is a trend of decrease for the enthalpy

( ∂σ α

of

structural

transition

as

the

size

of

nanoparticles

decreasing.

If

∂T ) P > ( ∂σ β ∂T ) , it shows that α phase is more stable at high temperatures but that at P

low temperatures for β phase, and the correlation between entropy of structural transition and size of nanoparticles has a same tendency with enthalpy.


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3. Experimental 3.1 Preparation of nano-CuFe2O4 The nano-CuFe2O4 was prepared by high temperature solid phase method. An amount of Cu(CH3COO)2·H2O and a stoichiometric FeC2O4·2H2O was grinded into powder in a mortar, and then add the cosolvent to stir for 48 h. After the cosolvent evaporates, it was grinded into powder again. At a constant heating rate of 5 °C/min, the powder was sintered at 900 °C in an atmosphere of air, then was taken out of muffle furnace at the respective reaction time to cool it down at room temperature. The reaction time and the cosolvent were changed to adjust the particle size of nano-CuFe2O4, which are shown in Table 1. Table 1: The different preparation conditions. Number

Calcination temperature /°C

Cosolvent

Reaction time / h

d / nm

1

900

cyclohexane

18

32

2

900

benzene

18

36

3

900

n-propanol

18

43

4

900

ethanol

24

60

5

900

ethanol

42

79

3.2 Characterization of nano-CuFe2O4 Figure 1 shows the XRD patterns of the as-prepared nano-CuFe2O4 samples. The synthesized samples were tetragonal phase nano-CuFe2O4, which is consistent with the standard diffraction card JCPDS (34-0425) and can be proved by the three peaks around 35° and the two peaks around 30°, however, there is only one peak for cubic CuFe2O4. The secondary peaks around 33 degree are α-Fe2O3, which are due to the ferrites slowly decompose into α-Fe2O3 above a calcination temperature of 500 °C, and can be slowly dissolved and disappeared at 900 °C.25 The average crystallite sizes of nano-CuFe2O4 calculated by Scherrer Formula are 32, 36, 43, 60 and 79 nm, respectively.



∗ α−Fe2O3

79 nm 60 nm

Intensity

43 nm 36 nm 32 nm cubic phase

∗

20

30

40

50

60

70

80

2θ/° Figure 1 The XRD patterns of nano-CuFe2O4 with different crystallite sizes

3.3 Processing of Experimental Data of Structural transition DSC (Q2000) was employed to determine the structural transition of nano-CuFe2O4 from tetragonal to cubic. As the Figure 2 shows, Teo is the temperature of structural transition. The ordinate value on the DSC curve is denoted as y1. Tb and Tf are the starting point and the finishing point of endothermic peak, respectively, and a straight line equation can be obtained from the two points, which corresponding value of Y-axis is labeled as y2. Then the difference between y1 and y2 is ∆y . Ti is the midpoint of ∆T .

Tb Heat Flow

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Teo

Teof

Tf

y1 ∆T

y2 Temperature

Figure 2 DSC diagram of structural transition According to the Trapezoidal Formula, the area Qi of the shaded part can be approximated. Hence, the enthalpy and entropy of structural transition can be obtained by integral, respectively, as follow,

∆H = ∫ δ Q = ∑ δ Q i


(12)

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∆S = ∫

δQ T

=∑

δ Qi Ti

(13)

3.4 Test of magnetic property Magnetic measurements were performed by Magnetic Property Measurement System [MPMS (SQUID) XL].

4. Results and Discussion 4.1 Effect of sizes on thermodynamics of structural transition The test of structural transition of nano-CuFe2O4 was carried out using DSC. Figure 3 shows the recorded DSC curves from 650 K to 730 K for nano-CuFe2O4 with varying sizes. According to the recorded DSC curves of nano-CuFe2O4 with varying sizes, the temperatures of structural transition were measured, the enthalpy and entropy were obtained based on the Eq. (12) and (13), shown in Table 2.

79 nm -1

Heat Flow/(W ⋅g )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


60 nm 43 nm 36 nm 32 nm scan direction

Exo Up

650 660 670 680 690 700 710 720 730 Temperature/K

Figure 3 DSC curves of nano-CuFe2O4 with varying size of nanoparticles As shown in Figure 3 and Table 2, the temperature of structural transition moves along the opposite scanning direction with the size of nano-CuFe2O4 decreases, integral enthalpy, integral entropy of structural transition decrease accordingly. And the structural transition temperature only decreased by 11.4 K from 689.95 to 678.55 K, but the structural transition enthalpy reduced by 536.6 J·mol-1 from 756.7 to 220.1 J·mol-1.



Table 2 The Teo, ∆H and ∆S of structural transition for nano-CuFe2O4 with varying sizes. Number

d /nm

d −1 /nm

Teo/K

∆H /J·mol-1

∆S /J·mol-1·K-1

1

32

0.0313

678.55

220.1

0.067

2

36

0.0278

682.15

310.3

0.076

3

43

0.0233

683.35

399.0

0.091

4

60

0.0167

686.35

574.1

0.129

5

79

0.0127

689.95

756.7

0.206

-1

4.2 Size dependence the temperature of structural transition The curve of the temperature of structural transition (Teo) versus the reciprocal of size of nanoparticles was shown in Figure 4.

690 688 686

T eo /K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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684 682 680 678 0.010

0.015

0.020 -1

0.025

0.030

0.035

-1

d /nm

Figure 4 Variation of temperature of structural transition with reciprocal of size of nano-CuFe2O4 As illustrated in Figure 4, as the size of nano-CuFe2O4 decreasing, the temperature of structural transition decreases and it presents a linear correlation with the reciprocal of sizes, which is consistent with the experimental results26 and the theoretical conclusion in literature.27 The intersection point between the linear correlation equation and the Y-axis is the temperature of structural transition for bulk CuFe2O4, with a value of 696.4 K. Jiang et al.16 attributed the reduction of the temperature of structural transition to the change of the surface phenomenological coefficients α and β with the particle size. Our group holds that the nanoparticles with smaller particle size have enormous surface energy and contribute greatly to the Gibbs free energy, and more, the lattice defects of smaller particles reduced the energy needed for the structural transition. Hence, the structure transition occurs at lower temperature


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for nanoparticles compared with bulk counterparts. However, Köferstein et al.28 obtain an opposite conclusion: the structural transition temperature increases with the decreasing particle sizes. By comparison, it was found that the literature used porous nano-CuFe2O4 as a research system, while our group used solid nano-CuFe2O4 as a system. The curvature radius for outer surface and inner micropore of nanoparticles is different, positive and negative, respectively. Therefore, the correlation between the temperature of structural transition and the size of solid nanoparticles is opposite to that of the porous nanoparticles.

4.3 Size dependence the enthalpy of structural transition A plot of the enthalpy of structural transition ( ∆H ) versus size of nanoparticles was shown in Figure 5. 800

-1

)

700

∆Η/(J⋅mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


600 500 400 300 200 0.010

0.015

0.020 -1

0.025

0.030

0.035

-1

d /nm

Figure 5 Variation of enthalpy of structural transition with reciprocal of size of nano-CuFe2O4 It can be revealed in the Figure 5, the size of nano-CuFe2O4 can remarkable influence the enthalpy of structural transition: the enthalpy of phase transformation decreases by about 3.5 times when the particle size is decreased by 2.5 times，which is accord with those reported in literatures.15,27,29 And there is a linear correlation between the enthalpy of structural transition and the reciprocal of size of nanoparticles, which are in good agreement with the above experimental results. The intersection point between the linear correlation equation and the Y-axis is the enthalpy of structural transition for bulk CuFe2O4, with a value of 1070.5 J· mol-1.

4.4 Size dependence the entropy of structural transition Figure 6 shows variation of structural transition entropy ( ∆S ) with reciprocal of size of



nano-CuFe2O4.

-1

∆ S/(J ⋅ mol ⋅K )

0.20

-1

0.15

0.10

0.05 0.010

0.015

0.020

0.025

-1

0.030

-1

d /nm

Figure 6 Variation of structural transition entropy with reciprocal of size of nano-CuFe2O4 As shown in Figure 6, with the size of nanoparticles decreases, the entropy of structural transition decreases, which is consistents with the experimental results and theoretical calculation of size dependence the structural transition entropy reported in literature.16 And the entropy of structural transition varies linearly with the reciprocal of size of nanoparticles.

4.5 Size dependence the magnetic properties Figure 7 shows the magnetization (M) of nano-CuFe2O4 with varying sizes, measured at room temperature, on the applied magnetic field (H). The inset shows M versus H in a small field range. The magnetic performance parameters for CuFe2O4 nanoparticles with varying diameters are shown in the Table 3. 30

10

32 nm 36 nm 43 nm 60 nm 79 nm

0 -10

10 0

-20

-1

20

32 nm 36 nm 43 nm 60 nm 79 nm

M/emu⋅g

-1

20

M/emu⋅g

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-10

-30

-20 -1000

-20000

-10000

0

-500

H/Oe 0 500

10000

1000

20000

H/Oe

Figure 7 Magnetization (M) of nano-CuFe2O4 with different sizes versus applied magnetic field (H) at room temperature


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Table 3 The magnetic performance parameters of nano-CuFe2O4 vary with sizes parameters

Saturated Magnetization

Coercivity

Remanence

Ms/ emu· g

Br/ Oe

Mr/ emu· g-1

32

23.4

1086.2

11.5

36

25.5

703.3

11.9

43

26.8

696.8

12.3

60

27.3

640.0

13.4

79

29.4

514.5

13.4

-1

size/nm

It is can be seen from Table 3 that tetragonal phase nano-CuFe2O4 is ferromagnetic materials. The size of nanoparticles has a huge impact on the magnetic performance parameters: as the size of nano-CuFe2O4 decreasing, the saturated magnetization and the remanence decrease, while the coercivity increases. The decrease in size of nanoparticles induces more serious surface defects, the magnetic responses accordingly become weaker, and then the saturation magnetization decreases.30-32 More, as the magnetic domain structure of nanoparticles transforms from multi-domain to single domain with particle size decreasing, the reverse magnetization transforms from the domain wall displacement to the magnetic moment rotation to enhanced coercive force.33 In addition, the large surface energy of nanoparticle and the increase in anisotropy at grain boundaries results in the increase in surface demagnetization and the decrease in remanence.

5. Conclusions The results show that, as the decrease of sizes, the temperature and the entropy as well as the enthalpy of structural transition of nano-CuFe2O4 decrease, and present linear variation with the reciprocal of sizes, respectively. Furthermore, the size of nano-CuFe2O4 can apparently influence the magnetic properties of nano-CuFe2O4: as the size of nano-CuFe2O4 decreasing, the saturated magnetization and the remanence decrease, while the coercivity increases.

Acknowledgments The authors are very grateful for the financial support from the National Natural Science Foundation of China (Nos. 21373147 and 21573157).



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Page 14 of 15

Page 15 of 15

Table of Contents graphic 800

+

3Vβ   ∂σβ  2Tbσβαβ  Tf σβ −Tb   + Cp,β (T ) dT  − 3  ∫Tb rβ   ∂T P

43 nm

∆ βα Sm = ∆βα Smb ( Tb ) +

36 nm

3Vα  ∂σ α  2σ αα α    +  rα  ∂T  P 3 

3V   ∂ σ β  2σ β α β  − β  +  + rβ   ∂ T  P 3 

32 nm

Tf

C p ,β (T )

Tb

T

∫

dT

0.21

700 0.18 600 0.15 500 0.12

400

0.09

300

0.06

200

650 660 670 680 690 700 710 720 730 Temperature/K

∆ S /(J ⋅ m o l -1 ⋅ K -1 )

60 nm

3Vα   ∂σα  2Tbσααα  σα −Tb   −  rα  3   ∂T P

∆ Η / ( J ⋅ m o l -1 )

∆βα Hm = ∆αβ Hmb ( Tb ) −

79 nm Heat Flow/(W ⋅ g -1 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.010

0.015

0.020 -1

0.025

0.030

0.035

-1

d /nm

The temperature, the enthalpy and the entropy of structural transition present linear variation with the reciprocal of sizes. And the experimental results are consistent with the above theory.


Effect of Size on the Structural Transition and Magnetic Properties of

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