site

, A

, Q

7; ae 2

it vmevityion

to determine the thermal conductivity of ferrites as a

imperfections, impurities and radiation through the material. Thetheory of thermal conductivities discussed earlier predicts that

and thermoelectric properties. Recently we have reported the

2. Experimental

The M-type SrFe12O19 with SiO2 (0.0, 0.5, 1.0, 1.5 wt.%)namely F-0.0, F-0.5, F-1.0, F-1.5, respectively, were prepared by

Available online at www.sciencedirect.com

08)the conductivity of an ideal dielectric above its Debye tem-perature is inversely proportional to the absolute temperature [3].fundamental material constant. Since thermal conductivity is astructural sensitive property, the constant obtained frommeasurements of polycrystalline aggregates are not generallyapplicable unless the effects of the microstructures on thesevalues are known. In the dielectric materials, heat is transferredby thermal vibrations of the lattice. Thermal conductivity of thebody is determined by inelastic collision and the scatter ofphonons, or in analogy with kinetic theory, by the mean free pathof the phonons. The factors which may affect thermalconductivity in ferrites are grain boundaries, pores, lattice

structural, magnetic and electrical properties of Si-added Sr-hexa ferrites [4]. The aim of present work is to measure thethermal conductivity, thermal diffusivity and specific heat perunit volume of the Sr-hexa ferrites as a function of temperatureusing TPS technique. These measurements are being reportedfor the first time to the best of our knowledge. It is expected thatthe change in thermal properties will throw light on an importantmaterial which can be used in thermo-technological applicationssuch as fire forewarning or as an integrating dosimeter.1. Introduction

M-type hexagonal ferrites, such as Sr (Ba) Fe12O19 have beenintensively investigated as a material for permanent magnets,high-density recording, magneto-optic media, and microwavedevices [1,2]. In recent years, a few investigators have attempted

At lower temperatures, the conductivity increases more rapidly,supporting the theoretical expectation that the Debye relation-ship will not hold below, Debye temperature. The phasetransition of the material is, in general, accompanied by manyanomalous physical properties. In a dielectric substance,anomalous are often found in specific heat, thermal conductivityKeywords: Sr-hexa ferrite; Transient plane source technique; Thermal conductivover the entire range of temperature under investigation. 2007 Elsevier B.V. All rights reserved.

PACS: 75.50.Gg; 72.15.Eb; 66.30.Xj; 65.40.Ba.ity; Thermal diffusivity; Heat capacityThermal transport properties offunction of

Shahid Hussain

Thermal Physics Laboratory, Department of Physics

Received 11 May 200Available onlin

Abstract

Thermal conductivity, thermal diffusivity, and heat capacity per unhave been measured using transient plane source (TPS) technique. Therange from 303K to 473 K. It has been noted that both thermal conducticapacity per unit volume (Cp) decreases. Addition of SiO2 concentrat

Materials Letters 62 (20 Corresponding author. Tel.: +92 51 2601014; fax: +92 51 90642240.E-mail addresses: jamshahid@yahoo.com, tpl.qau@usa.net (S. Hussain).

0167-577X/$ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.matlet.2007.07.056lica added Sr-hexa ferrites as amperature

sghari Maqsood

uaid-i-Azam University, Islamabad 45320, Pakistan

ccepted 16 July 2007August 2007

olume of silica added (SiO2=0.0, 0.5, 1.0, 1.5 wt.%) Sr-hexa ferritesasurements have been made at normal pressure and in the temperature() and thermal diffusivity () increase with temperature whereas heatin the Sr-ferrite increases the values of and but decreases the Cp

10021005www.elsevier.com/locate/matleta double sintering ceramic method using SrCO3, Fe2O3, SiO2.Final sintering of the specimens was carried out at 12005 Cfor 2 h in air. The details of the method of preparation along with

t ca

3

.00

rialthe physical characterization of these samples are reported byHussain and Maqsood [4].

The transient plane source (TPS) technique [5] was utilized tomeasure the thermal transport properties of the samples, because itallows the measurements without any disturbance form theinterfaces between the sensor and the bulk samples. Also,simultaneous measurement of thermal conductivity (), thermaldiffusivity (), and heat capacity per unit volume (Cp) is possible[5]. In this technique, a TPS-element made of 10 m-thick nickelfoil with an insulating layer made of 50 m-thick mica, on eachside of themetal pattern, is used both as constant heat source and asensor of temperature. For data collection, the TPS element of(20 mm diameter) sandwiched between two halves of the samesamples in a bridge circuit [6,7]. The TPS-element had aresistance of 5.00605 at room temperature and a temperaturecoefficient of resistance (TCR) of around 4.87103 K1.

The sample holder containing these samples is placed in afurnace having sensitivity of 1 K. After achieving the isothermalcondition in the sample, a constant current pulse of width 28 sand a height 0.19 mA is passed through the heating element.Owing to the change in average temperature of the sensor, thepotential difference across changes. The transient potentialdifference across the terminals is recorded by a digitalmultimeter and the current through the TPS sensor is noted as

Table 1Temperature dependent thermal conductivity (), thermal diffusivity () and hea

F-0.0 F-0.5

Temp(K)

Wm1

K10.001k mm2

S10.001CpMJ m3

K10.001

Wm1

K10.001k mm2

S10.001CpMJ m

K10

298 2.690 1.132 2.731 2.767 1.541 1.791323 2.806 1.517 1.845 2.921 1.659 1.755348 3.041 1.712 1.772 3.480 2.219 1.572373 3.243 1.922 1.682 3.687 2.456 1.485398 3.533 2.220 1.585 3.871 2.722 1.419423 3.711 2.532 1.462 4.017 2.912 1.375448 4.084 2.832 1.439 4.180 3.107 1.341473 4.322 3.247 1.329 4.385 3.327 1.318

S. Hussain, A. Maqsood / Matedescribed earlier [6]. The current in circuit is adjusted accordingto the nature of the sample material. Multiple readings atappropriate intervals are taken to ensure the accuracy of theresults. The TPS programme used here is capable of recordingthe temperature of the sample through the TPS sensor itself. Inaddition to this a sensitive Pt-100 thermometer is kept just abovethe sample pieces inside the furnace to monitor the temperatureof the sample. By recording the voltage drop for a particular timeinterval, detailed information about the thermal conductivity andthermal diffusivity of the test specimen is obtained. The heatcapacity per unit volume is then calculated form the relation

qCp kj 1

where is the mass density of sample. For thermal conduc-tivity measurements, each sample consisted of two identicalcircular tablets of the same specimen. The surfaces of thesamples were made smooth to have a good thermal contact withTPS-element and to minimize thermal contact resistance. Thethicknesses of the samples were chosen so as to satisfy theprobing depth criteria [8]. Taking into consideration the errorsof technique [7,9], standard deviations of the measurements andthe sampling errors, the thermal conductivity and thermaldiffusivity data contain errors of 5% and 7%, respectively. Theerrors in volumetric heat capacity are around 10%. The resultsof the thermo-physical measurements of the samples at differenttemperature and normal pressure are shown in Table 1.

3. Results and discussion

Thermal transport properties of the ferrites depend upon theirstructure, density, porosity, composition, temperature and pressure, etc.The temperature dependence of thermal conductivity, thermaldiffusivity, and heat capacity per unit volume was measured fromroom temperature i.e. 303 K to 473 K with 25 K intervals and theresults are shown in Table 1. It was observed that thermal conductivityof all the samples increases in the mentioned temperature range, asreported in literature [10,11], indicating that behavior may be intrinsicas shown in Fig. 1.

Thermal conductivity can be expressed as a sum of latticecomponent (l) and electronic component (e) [11,12] as

k kl ke 2

pacity per unit volume (Cp) of all the samples

F-1.0 F-1.5

1

Wm1

K10.001k mm2

S10.001CpMJ m3

K10.001

Wm1

K10.001k mm2

S10.001CpMJ m3

K10.001

3.674 1.613 2.255 4.101 1.791 2.2854.325 2.219 1.943 5.262 2.385 2.2014.466 2.503 1.789 5.402 2.497 2.1634.492 2.613 1.719 5.430 2.612 2.0724.968 2.922 1.702 5.625 2.832 1.9855.111 3.327 1.532 5.835 3.642 1.6075.530 3.722 1.480 6.451 4.225 1.5295.886 4.123 1.427 7.076 5.246 1.345

1003s Letters 62 (2008) 10021005The e values can be estimated from WeidmanFranz's law as

ke LTr 3where L is Lorentz number (2.45108 WK2 for free electrons),T temperature in K and is electrical conductivity at a giventemperature. Hence lcan be obtained using Eq. (2).

This is analogous with the electrical behavior in the semi conductingmaterials [12], in which by increasing temperature, free electrons arejumping from valance band to the conduction band in order to increasethe electrical conductivity. But at low temperature electronic contribu-tion to the thermal conductivity is very low as shown in Fig. 2.

Similar behavior is observed with conduction of heat in ferrites andalloys as reported earlier [1315]. Another factor to increase in thermalconductivity is attributed to the increase in number of phonons with therise in temperature which is the major portion. i.e. about 90% of totalthermal conductivity comparative to the free electrons at lowtemperature [13,14]. But at high temperature, the number of phononsincreases enough so that the phonon-phonon scattering occurs near Tc,

Fig. 1. Temperature dependent thermal conductivity for all the samples.

1004 S. Hussain, A. Maqsood / Materials Letters 62 (2008) 10021005this may be the cause of the decrease in thermal conductivity as noticedearlier [14,16]. The increase in thermal conductivity with addition ofSiO2 is also observed at room temperature as shown in Fig. 3. This maybe due to the fact that some of the SiO2 decomposes the SrFe12O19phase into SrSiO3 and Fe2O3 phases. Most of the added silica settleddown at grain boundaries and junctions. Since Fe2O3 and SiO2 havegreater thermal conductivity values (20 Wm1 K1 and 7.68 Wm1

K1, respectively [17,18]) than the pure ferrites (2.92Wm1 K1 [19]),an increase in thermal conductivity of the said ferrite system has beenobserved with the successive addition of SiO2.

Another increasing factor may be due to the fact that SiO2 is graingrowth inhibitor, resulting into denser structure [4,20]. A Similarbehaviour was observed with the thermal diffusivity as shown inTable 1, which has the direct relation with the thermal conductivityaccording to Eq. (1).

Heat capacity per unit volume of the studied samples has the inverserelation with and . Thus it has decreasing trend with the rise intemperature from 303K to 473K as shown inTable 1. Since good thermalconductor will conduct maximum heat to the surroundings and have lesscapacity to store heat. Fig. 4 shows the relationship between the densityand thermal transport properties. Eq. (1) shows a direct relationship withthermal conduction phenomenon and density. Fig. 4 shows that the heatcapacity per unit volume decreases with bulk density.

It is to be noted that in case of high heat capacity, like F-0.0 sample

(Table 1), thermal conductivity decreases due to which temperatureraises that results in magnetic moments misalignment and hence loss in

Fig. 2. Temperature dependence of the thermal conductivity of Sr-hexa ferritecontribution from electrons and phonons.magnetic properties may be expected. The studied Sr-hexa ferrites maybe beneficial for its permanent magnet application at high temperature.

4. Conclusions

To summarise the current study, it was noticed that by theaddition of SiO2 in the Sr-hexa ferrite system, thermalconductivity increases from 2.690 Wm1 K1 to 4.101 Wm1

K1 not only at room temperature but also with increasingtemperature. The increase in with rise in temperature is due tothe free electrons and lattice vibrations (phonons). Thermaldiffusivity also increases from 1.132 mm2 S1 to 1.791 mm2

S1 by the addition of SiO2 at room temperature. Maximummeasuring temperature was 473 K due to setup limitations, so itis suggested that this increase in thermal conductivity anddiffusivity would be up to Tc, after that these values are expectedto fall. Heat capacity per unit volume decreased from 2.731 MJm3 K1 to 2.285 MJ m3 K1 at normal temperature andpressure.

Acknowledgements

Fig. 3. Variations in thermal transport properties with silica addition at normaltemperature and pressure.The authors would like to acknowledge Higher EducationCommission (HEC) Pakistan and Quaid-i-Azam UniversityResearch Fund (URF) for financial support. The author (Shahid

Fig. 4. Variation of thermal conductivity , thermal diffusivity , and heatcapacity per unit volume Cp with density at normal temperature and pressure.

Hussain) is particularly grateful to HEC for the grant of Ph. Dscholarship under the 200 Merit Scholarship Scheme and Mr.Aurangzeb is thanked for fruitful discussion.

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1005S. Hussain, A. Maqsood / Materials Letters 62 (2008) 10021005

Thermal transport properties of silica added Sr-hexa ferrites as a function of temperatureIntroductionExperimentalResults and discussionConclusionsAcknowledgementsReferences