1-temperature dependence of effective thermal conductivity and effective thermal diffusivity of...

8/12/2019 1-Temperature Dependence of Effective Thermal Conductivity and Effective Thermal Diffusivity of Ni-Zn Ferrite

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Acta Materialia 51 (2003) 25692576 www.actamat-journals.com

Temperature dependence of effective thermal conductivityand effective thermal diffusivity of Ni-Zn ferrites

G.P. Joshi, N.S. Saxena , R. Mangal

Condensed Matter Physics Laboratory, Department of Physics, University of Rajasthan, 5-6, Vigyan Bhawan, Jaipur-302004,

India

Received 6 August 2002; accepted 24 December 2002

Abstract

Measurement of thermal transport properties of nanocomposites of Ni-Zn ferrite in a copolymer matrix of aniline-formaldehyde has been made using transient plane source (TPS) technique. In the temperature range from room tempera-ture to 140C both effective thermal conductivity (l

e) and effective thermal diffusivity (c

e) increase with increase in

temperature and become maximum at a particular temperature which is a characteristic temperature for a given material.For further increase of temperature thel

eand c

edecreases slowly. An effect has also been made to predict theoretically

these values by an empirical model. Addition of zinc concentration in the composite decreases the value ofleand c

e

over the entire range of temperature under investigation. It has also been found that the temperature at which a structural

and bond strength change occurs depends on zinc concentration. 2003 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

Keywords: Nanocomposites; Transient plane source technique; Effective thermal conductivity; Effective thermal diffusivity

1. Introduction

In the past few years nanocomposite materialshave become one of the most extensively studied

materials. Nanocomposite materials composed ofoxides and conducting polymers have brought outmore fields of applications such as smart windows,toners in photocopying, rechargeable batteries[1],etc. Thermal transport properties of oxides havewide ranging applications, such as in supercon-

Corresponding author. Tel.: +1-91-141-511239; fax: +1-91-141-515828.

E-mail address:[email protected] (N.S. Saxena).

1359-6454/03/$30.00 2003 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

doi:10.1016/S1359-6454(03)00056-9

ducting materials, nuclear reactor etc. It is observedthat in powder systems the values of effective ther-mal conductivity and effective thermal diffusivityvary with the variation of particle size [2] and

porosity of the system. Nanomaterials, particularlywith magnetic properties, have their applications incolor imaging, ferrofluids, bioprocessing, medicaldiagnosis and electromagnetic wave absorption[3,4]etc. The nanocomposites are one of the classof nanomaterials. The nanomaterials can beamorphous in nature and they can be distinguishedfrom the nanocrystalline and nanophase materialsas only one phase exists. Physical properties ofnanophase materials are presently of great scien-tific interest [5]. Thus nanocomposites are formed


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2570 G.P. Joshi et al. / Acta Materialia 51 (2003) 25692576

by combining conducting polymers and inorganic

nanoparticles. The properties of nanocomposite of

such kind are strongly dependent on concentration

of polymer [6]. Optical properties such as opticalband gaps have been done in these samples. Nano-

composites of aniline formaldehyde have beenfound to have direct band gap which increases withthe concentration of zinc in the composite [7]. Sothe present study is aimed at studying the variation

in thermal properties of these nanocomposites

materials over a temperature range from 30 to140C and at normal pressure using transient planesource (TPS) technique.

2. Experimental details

Nanocomposites of Ni-Zn ferrite in a copolymer

matrix of aniline-formaldehyde were synthesized at

room temperature by using a novel chemicalmethod reported elsewhere[8].The nanocomposi-

ties of Ni1-x ZnxFe2O4 ferrites with x = 0.0, 0.2,0.4, 0.6, 0.8 and 1.0 were synthesized in a copoly-mer matrix (containing three different monomers)of aniline-formaldehyde. As a typical preparation,

sample S1 (x = 0) was synthesized by treating the

aqueous solution of aniline (0.10 mole), hydro-chloric acid (0.12 mole), formaldehyde (0.10 mole)and nickel (0.189 mole) taken according to the

stoichiometry. The resulting solution was stirred

thoroughly and added to 10% solution of alkali.The precipitated composite was washed repeatedly

with the distilled water till the filtrate was free ofalkali (pH = 7.5) and then dried in air. Similarly,the samples S2S6 (x = 0.2, 0.4, 0.6, 0.8 and1.0) were synthesized using the same procedure by

varying the quantities of nickel and zinc according

to the stoichiometry. Pellets of thickness 2 mm anddiameter 12 mm were prepared from the powdered

materials by a pressure of 4.33 108 Pascal. Thesample holder(Fig. 1)containing these samples is

placed in a furnace having sensitivity of 1 K. Afterachieving the isothermal conditions in the sample,a constant current pulse of width 15 s and height

0.0792 Amp is passed through the heating element.

The measurements reported in this paper were per-formed with a TPS element of the type shown in

Fig. 2. It is made of 10 m-thick nickel foil with

Fig. 1. Sample holder.

Fig. 2. Schematic diagram of TPS sensor.

an insulating layer made of 50 m-thick kapton,on each side of the metal pattern. Evaluation of

these measurements was performed in a way that

was outlined by Gustafsson[9].No influence couldbe recorded fromelectrical connections, which are

shown in Fig. 3. These connecting leads had the

same thickness as the metal pattern of the TPS

Fig. 3. Schematic diagram of electrical circuit for simul-

taneous measurements of effective thermal conductivity and

effective thermal diffusivity.


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2571G.P. Joshi et al. / Acta Materialia 51 (2003) 25692576

element. Each TPS element had a resistance at

room temperature of about 3.26 and a tempera-

ture coefficient of resistance (TCR) of around

4.610

3K

1. Owing to the change in average tem-perature of the sensor, the potential difference

across it will change. The transient potential differ-ence across the terminals is recorded by a digitalmultimeter, and the current through the TPS sensorwith a digital power supply. The current in the cir-

cuit is adjusted according to the nature of the sam-

ple material. Multiple readings at appropriate inter-vals are taken to ensure the accuracy of the results.

The TPS programme used here is capable of rec-

ording the temperature of the sample through the

TPS sensor itself. In addition to this a sensitivethermometer is kept just above the sample pieces

inside the furnace to monitor the temperature ofthe sample.

3. Transient plane source (TPS) theory

The TPS method consists of an electrically con-

ducting pattern(Fig. 2)in the form of a bifilar spi-ral, which also serves as a sensor of the tempera-ture increase in the sample. The sensor is

sandwiched between the thin insulating layers ofkapton. Assuming the conductive pattern to be inthe y-z plane of a co-ordinate system inside thesample, the rise in the temperature at a point y-z

at time t due to an output power per unit area Qis given by [9]

T(y,z,) 1

43/2a

0

d

2AdydzQ(y,z,t (1)

s2a2

exp(yy)2(zz)2

4s2a2 where (t - t) = 2 a2 , q = a2 / , and = [t /]1/2. a is the radius of the hot disc which gives ameasurement of the overall size of resistive pattern

andq is known as the characteristic time. s is thevariable parameter, l is the thermal conductivityin units of W/mK and cis the thermal diffusivityin unit of mm2/s of the sample material. The tem-

perature increase T (y,z,t) because offlow of cur-rent through the sensor gives rise to a change in

the electrical resistance R(t) which is given as

R(t) R0 T() (2)

where Ro is resistance of TPS element before thetransient recording has been initiated, a is TCRand T() is the properly calculated mean value ofthe time-dependent temperature increase of theTPS element. During the transient event, T()canbe consider to be a function of time only, where

as in general it will depend on such parametersas the output power in TPS element, the design

parameters [10] of the resistive pattern, and the

thermal conductivity and thermal diffusivity of sur-roundings. T() is calculated by averaging theincrease in temperature of TPS element over the

sampling time because the concentric ring sources

in TPS element have different radii and are placedat different temperatures during the transient rec-

ording.It is possible to write down an exact solution[9]

for the hot disc if it is assumed that the disc con-tains a number m of concentric rings as sources.From the ring source solution [11] we immedi-

ately get

T() P

3/2aDs() (3)

whereDs() [m(m 1)]

2 (4)

0

d

2m

I 1

1m

k 1

k exp(l2 k2)

42m2 L0 lk

22m2In Eq. (4), P0is the total output power, L0 is the

modified Bessel function and l, k are the dimen-sions of the resistive pattern. To record the poten-

tial difference variations, which normally are of theorder of a few millivolts during the transient rec-ording, a simple bridge arrangement as shown in

(Fig. 3)has been used. If we assume that the resist-ance increase will cause a potential difference vari-

ation U(t) measured by the voltmeter in thebridge, the analysis of the bridge indicates that

E(t) Rs

Rs RoIoR(t) (5)

Rs

(Rs Ro)

IoaRoPo3/2a

Ds()

where


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E(t) U(t)[1 C.U(t)]1 (6)

and

C 1

RsIo1 Rp(Rs Ro) Rp (7)

Thedefinition of various resistances is found inFig. 3. Rp is the lead resistance, Rs is a standardresistance with a current rating that is much higher

than Io, which is the initial heating current through

the arm of the bridge containing the TPS-element.g is the ratio of the resistances in two ratio armsof the bridge circuit, which is taken to be 100 in

the present case.

4. Results and discussion

Results of effective thermal conductivity andeffective thermal diffusivity are given in Tables 1

and 2. It is interesting to note that the value of

effective thermal conductivity and effective ther-mal diffusivity are for the glass pallets made at 5

tone of load. It has been observed [12] that thevalue increases slightly with the increasing press-

ure or load used for making the pallets. The vari-ation of effective thermal conductivity and effec-

tive thermal diffusivity with temperature for

Table 1

Experimental and theoretical value of effective thermal conductivity (W/mK) vs. temperature

Sample no. Effective thermal Temperature (C)conductivity (W/m-K)

50 80 100 120 130 140

S1 Experimental 0.30 0.32 0.34 0.36 0.34 0.33Theoretical 0.30 0.31 0.34 0.36 0.35 0.33

S2 Experimental 0.29 0.31 0.33 0.35 0.33 0.31

Theoretical 0.29 0.29 0.33 0.35 0.34 0.31

S3 Experimental 0.28 0.30 0.32 0.34 0.32 0.30

Theoretical 0.28 0.28 0.32 0.34 0.32 0.30

S4 Experimental 0.27 0.29 0.31 0.33 0.31 0.29

Theoretical 0.27 0.27 0.31 0.33 0.32 0.29

S5 Experimental 0.26 0.28 0.30 0.32 0.30 0.28

Theoretical 0.26 0.26 0.30 0.32 0.31 0.28

S6 Experimental 0.25 0.27 0.29 0.31 0.29 0.27

Theoretical 0.25 0.25 0.29 0.31 0.30 0.27

nanocomposities of Ni1-xZnxFe2O4 ferrites with

x= 0.0,0.2, 0.4, 0.6, 0.8 and 1.0 is shown in Figs.4 and 5. It is seen that the effective thermal con-

ductivity of all the composites shows a similartrend of almost linear increase with temperature to

a peak value. The peak values are observed ataround 120 C for all compositions. The value ofeffective thermal conductivity then decreases withthe increase of temperature. Experimental value of

the effective thermal conductivity and effective

thermal diffusivity at room temperature is 0.29W/mK with x=0.0 and decreases with the increaseof concentration of zinc to 0.24 W/mK for x =1.0. Nanomaterials can be polycrystalline or

amorphous in nature and may belong to inorganic,organic or combinations of inorganic and organic

classes of materials. Inorganic nanomaterialsinclude metal and alloys, semiconducting oxides,

magnetic oxides (ferrites, ferrofluds) etc. Propertiesin inorganic nanomaterials arise due to contri-bution by individual nanoparticle as well as their

combination due to peculiar structure and abnor-

mal phase state. These samples are prepared at lowtemperatures by sol-gel technique, which upon

heating at high temperatures gives rise to singlephase crystalline or multiphasic crystalline cer-

amics. These materials thus exhibit properties aris-ing due to nanometer size scale or large density ofdefects. On increasing the concentration of zinc,


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Table 2

Experimental and theoretical value of effective thermal diffusivity (mm2/s) vs. temperature

Sample no. Effective thermal Temperature (C)diffusivity (mm2/s)

50 80 100 120 130 140

S1 Experimental 0.19 0.21 0.23 0.26 0.24 0.22

Theoretical 0.19 0.20 0.23 0.26 0.24 0.22

S2 Experimental 0.18 0.20 0.22 0.24 0.22 0.21

Theoretical 0.18 0.19 0.22 0.24 0.23 0.21

S3 Experimental 0.17 0.19 0.21 0.23 0.21 0.19

Theoretical 0.17 0.17 0.21 0.23 0.22 0.19

S4 Experimental 0.15 0.17 0.19 0.21 0.20 0.18

Theoretical 0.15 0.15 0.19 0.21 0.19 0.18

S5 Experimental 0.13 0.15 0.17 0.19 0.18 0.16

Theoretical 0.13 0.13 0.17 0.19 0.17 0.16S6 Experimental 0.12 0.14 0.16 0.17 0.15 0.14

Theoretical 0.12 0.13 0.16 0.17 0.16 0.14

Fig. 4. Temperature variation of effective thermal conduc-

tivity of different zinc concentration.

the value of saturation magnetization increases butexchange interactions decrease between the ions on

the two sites thereby causing decrease in the Curietemperature. The experimental results of tempera-ture dependence of effective thermal conductivity

and effective thermal diffusivity in the temperature

range from 50 to 140 C of all the samplespresented inFigs. 4 and 5. The effective value of

thermal conductivity (Fig. 4) initially shows a

Fig. 5. Temperature variation of effective thermal diffusivity

of different zinc concentration.

gradual linear increase, reaches a maximum and

then a decreasing trend is observed for all the com-positions with temperature. In the temperature

region before and after the peak in the effectivethermal conductivity vs. temperature curve, struc-ture scattering, which is temperature independent,

play an important role in the thermal resistance.

The observed variation in effective thermal con-ductivity is explained on the basis of various

phonon scattering mechanisms [13,14] viz. struc-


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tural scattering, stray scattering and chain defect

scattering. It has also observed that the values of

effective thermal conductivity are lower for the

higher concentration of zinc in the matrix for theentire range of temperature under investigation. It

has already been noted that as the concentration ofthe zinc increases in the sample the Curie tempera-ture decreases. The decrease in the Curie tempera-ture of these samples is indicative of the fact that

ferromagnetic nature, which depends upon the for-

mation of close domains of magnetic momentswith rigid boundaries, decreases because of

inclusion of lighter diamagnetic particles of zinc.

This tends towards the randomization of magnetic

moments, which produces non-rigid loose struc-tures with higher porosity of the sample. Thus, the

effective thermal conductivity decreases as weinclude more and more concentration of zinc in the

nanocomposities of Ni-Zn ferrites. Effective ther-

mal diffusivity vs. temperature plotfor all the com-positions are presented in Fig. 5. It is seen that

thermal diffusivity also increases linearly but

slowly with temperature before the peak of thermaldiffusivity, proceeds towards a maximum, which

occurs almost at the same temperature where effec-tive thermal conductivity also shows its maximum

or peak value. For further increase of temperatureover the characteristic temperature T0 (where leand ce show their maxima) the effective thermalconductivity and thermal diffusivity decreases very

slowly. In the low temperature region below T0thetemperature dependence of effective thermal con-

ductivity and effective thermal diffusivity is con-

trolled by the variation of phonon mean free paths.By means of a least squares fit to the experimentaldata of effectivel andcas a function of tempera-ture, as plotted in Figs. 6 and 7 for sample S1 to

S6, empirical relationships have been developedforthe theoreticalprediction ofl and c. As showninTables 3 and 4 these are given as:

e A B(TTo) C(TTo)2 (8)

D(TTo)3

e a b(TTo) c(TTo)2 (9)

d(TTo)3

where A, B, C, D, a, b, c and d are constants calcu-

lated by experimental conditions. T is the tempera-

Fig. 6. Temperature variation of theoretical and experimental

value of effective thermal conductivity of sample S1 and S6.

Fig. 7. Temperature variation of theoretical and experimental

value of effective thermal diffusivity of sample S1 and S6.

ture of the composite in absolute temperature units.Observed variation in le and ce with temperaturecan be explained by considering the effect of tem-perature on structural units in a phenomenologicalmanner. In the temperature range below T0 the

temperature dependence ofle andce is controlledby the variation of phonon mean free path due tostructure scattering, stray scattering and chain

defect scattering. For temperatures below To,struc-


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Table 3

Value of constants A, B, C, and D in Eq. 8 for the effective thermal conductivity of nanocomposites

Sample no. Peak value of Constants for effective thermal conductivity of nanocomposites

temperature (C)

A (W/m-K) B (W/m-K2) C (W/m-K3) D (W/m-K4)

S1 120 0.36 1.0105 6.2105 7.2107

S2 120 0.35 1.5104 7.5105 8.6107

S3 120 0.34 1.5104 7.5105 8.6107

S4 120 0.33 1.5104 7.5105 8.6107

S5 120 0.32 1.5104 7.5105 8.6107

S6 120 0.31 1.5104 7.5105 8.6107

Table 4Value of constants a, b, c and d in Eq. (9) for the effective thermal diffusivity of nanocomposites

Sample no. Peak value of Constants for effective thermal diffusivity of nanocomposities

temperature (OC)

a (mm2/s) b (mm2/s-K) c (mm2/s-K2) d (mm2/s-K3)

S1 120 0.26 1.7104 8.7105 10.8107

S2 120 0.24 8.0104 6.2105 7.5107

S3 120 0.23 1.5104 7.5105 8.6107

S4 120 0.21 1.3104 6.2105 3.8107

S5 120 0.19 1.3104 6.2105 3.8107

S6 120 0.17 3.4104

5.0105

4.0107

ture scattering becomes predominant besides chain

defect scattering, scattering due to defects intro-duced by blends and relatively smaller length of

chain segments. With rising temperature the poly-

meric chain becomes straighter. Therefore, meanfree path increases, resulting in the increase ofleandcein this temperature range.Figs. 6 and 7alsoshow the variation ofle and ce with temperature

as predicted by empirical relations 8 and 9for sam-ple S1 and S6. It is clear from Figs. 67 that theagreement, between the predicted values ofle andce using the empirical relation and the results ofexperiment, is very good.

5. Conclusions

From the results of the said study it can be con-

cluded that effective thermal conductivity and

effective thermal diffusivity of Ni-Zn ferrites in a

copolymer matrix of aniline formaldehyde dependboth on the temperature and the concentration of

zinc in the composite. Zinc being a diamagnetic

material, when added to composite in large con-centrations, produces randomisation of the mag-

netic moments and hence loose non-rigid structures

which are resposible for the observed decrease of

effective thermal conductivity and diffusivity ofthe nanocomposite.

References

[1] Fried JR. Polymer Science and Technology. New Delhi:

Prentice Hall India, 1999 p. 461.

[2] Predeep P, Saxena NS. Physica Scripta 1997;55:634.

[3] Mathur R, Parihar M, Vadera SR, Kumar N. J Magnetics

Soc Jpn 1998;22(Supplement S1):273.


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[4] Vadera SR, Parihar M, Negi SC, Kumar N. Smart

Materials Structure and MEMS Proc SPIS 1998;369:3321.

[5] Mathur R, Sharma DR, Vadera SR, Kumar N. Bulletin of

Materials Science 1999;22(6):991.

[6] Suri K, Annapoorni S, Tandon RP. Bulletin of Materials

Science 2001;24(6):563.

[7] Joshi GP, Mangal R, Saxena NS, Sharma TP. Indian Jour-

nal of Pure and Appl Physics 2002;40:297.

[8] Mathur R, Sharma DR, Vadera SR, Gupta SR, Sharma

BB, Kumar N. Nanostruct Mater 1999;11(5):677.

[9] Gustafsson SE. Rev Sci Instrum 1991;62:797.

[10] Gustafsson SE, Suleiman B, Saxena NS, Haq IU. High

TempHigh Press 1991;23:289.

[11] Carslaw HS, Jaeger JC. Conduction of heat in solid.

Oxford: Oxford University Press, 1959.

[12] Singh K, Saxena NS. Presented in II National Conference

on Thermophysical Properties, Jaipur, Sept. 1921, 2002.

[13] Saxena NS, Pradeep P, Mathew G, Thomas S, Gustafsson

M, Gustafsson SE. European Polymer Journal

1999;35:1687.

[14] Dashora P, Saxena NS, Saksena MP, Sharma KB, Sachdev

K, Pradhan PR, Ladiwala GD. Physica Scripta

1992;45:399.

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