Simultaneous Measurements of Thermal Conductivityand Diffusivity of Se85–xTe15Sbx (x == 2, 4, 6, 8, and 10)Chalcogenide Glasses at Room Temperature

K. Singh (a), N. S. Saxena1Þ (a), and N. B. Maharjan (b)

(a) Condensed Matter Physics Laboratory, Department of Physics,University of Rajasthan, Jaipur, India

(b) Central Department of Physics, Tribhuvan University, Kirtipur, Kathmandu, Nepal

(Received August 7, 2001; in revised form October 24, 2001; accepted October 29, 2001)

Subject classification: 61.43.Fs; 66.30.Xj; 66.70.+f; S8

Measurements of thermal conductivity (l) and thermal diffusivity (c) of Se85––xTe15Sbx (x = 2, 4, 6,8, and 10) thin pellets, prepared at a constant pressure of 4.33 � 108 Pa, have been carried out atroom temperature using the transient plane source (TPS) technique. The measured values of bothl and c have been used to determine the specific heat per unit volume (rcp) of these glasses in thecomposition range of investigation. The variation of l and c is found to have a maximum at 4 at%Sb. This is suggestive of the fact that 4 at% of Sb can be considered as a critical composition atwhich the alloy becomes chemically ordered and maximum thermal stable than at other composi-tions. Further addition of Sb in the alloy decreases the values of thermal conductivity and thermaldiffusivity. Specific heat per unit volume of the glass under investigation have been found to beminimum at 4 at% of Sb and increases with the further addition of Sb in the alloy. This behaviouris explained on the basis of bond formation between Se and Sb at different compositions.

1. Introduction

Great attention has been paid to chalcogenide glasses in recent years mainly due to theirwide range of applications as solid state devices both in the scientific and technologicalfield [1]. These glasses exhibit unique IR-transmission and electrical properties that makethem useful for several applications such as threshold switching, memory switching, inor-ganic photoreceptors, IR-transmission and detection through lenses and optical waveguides, e.g. in welding and surgery [2]. Especially Selenium alloys exhibit a unique prop-erty of reversible transformation. This property makes these systems very useful in opticalmemory, X-ray imaging and photonics. The addition of Sb as third element in differentpercentage in Se–Te binary chalcogenide glasses produces stability of these glasses [3].The effects of an additive to binary glasses have been extensively studied [4–6].

However, efforts to simultaneously measure the thermal conductivity l and thermaldiffusivity c have not been made so far. In the present work an investigation has beenundertaken to study the variation of l, c, and specific heat per unit volume rcp of thesesamples with composition. The transient plane source (TPS) technique was used for themeasurement of l and c, which was developed by Gustafsson [7] as an improvementover the transient hot strip (THS) method.

2. Transient Plane Source (TPS) Theory

The TPS technique has proved to be a precise and convenient method for measuringthe thermal transport properties of electrically insulating materials. The TPS method

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phys. stat. sol. (a) 189, No. 1, 197–202 (2002)

1) Corresponding author; e-mail: n_s_saxena@hotmail.com

consists of an electrically conducting pattern (Fig. 1) in the form of a bifilar spiral,which also serves as a sensor for the temperature increase in the sample. In Fig. 1,K-4521 is the design number of the sensor where ‘K’ stands for kapton. The sensor issandwiched between thin insulating layers of kapton. Assuming the conductive patternto be in the y–z plane of a coordinate system, the rise in the temperature at a point y,z at time t due to an output power per unit area Q is given by [7]

DTðy; z; tÞ ¼ 1

4p3=2al

ðt0

ds

s2

ðA

dy0 dz0 Q y0; z0; t � s2a2

c

� �exp

�ðy � y0Þ2 � ðz � z0Þ2

4s2a2

!;

ð1Þ

where c (t � t0) = s2a2, q = a2/c, t = [t/q]1/2, a is the radius of the hot disc which gives ameasurement of the overall size of the resistive pattern, q is known as the characteristictime, s is a constant variable, l is the thermal conductivity in units of W/mK, and c isthe thermal diffusivity of the material in units of m2/s. The temperature increase DT(y,z, t) because of the flow of current through the sensor gives rise to a change in theelectrical resistance DR(t) which is given as

DRðtÞ ¼ aR0DTðtÞ , (2)

where R0 is the resistance of the TPS element before the transient recording has beeninitiated, a is the temperature coefficient of resistance (TCR), and DTðtÞ is the prop-erly calculated mean value of the time dependent temperature increase of the TPSelement. During the transient event, DTðtÞ can be considered to be a function of timeonly, whereas in general it will depend on parameters such as the output power in theTPS element, the design parameters [8] of the resistive pattern, and the thermal con-ductivity and thermal diffusivity of surroundings. DTðtÞ is calculated by averaging theincrease in temperature of the TPS element over the sampling time because the con-centric ring sources in the TPS element have different radii and are placed at differenttemperatures during the transient recording.

It is possible to write down an exact solution [7] for the hot disc if it is assumed thatthe disc contains a number m of concentric rings as sources. From the ring source solu-tion [9] we immediately get

DTðtÞ ¼ P0

p3=2alDsðtÞ ; ð3Þ

where

DsðtÞ ¼ m m þ 1ð Þð Þ�2ðt0

ds

s2

Pml¼1

lPmk¼1

k exp�ðl2 þ k2Þ

4s2m2L0

lk

2s2m2

� �� �� �: ð4Þ

198 K. Singh et al.: Thermal Conductivity and Diffusivity of Se85––xTe15Sbx Chalcogenide Glasses

Fig. 1. Schematic diagram of TPS sensor

In Eq. (4), P0 is the total output power, L0 is the modified Bessel function, and l, kare the dimensions of the resistive pattern. To record the potential difference variations,which normally are of the order of a few mV during the transient recording, a simplebridge arrangement as shown in Fig. 2 has been used. If we assume that the resistanceincrease will cause a potential difference variation DU(t) measured by the voltmeter inthe bridge, the analysis of the bridge indicates that

DEðtÞ ¼ Rs

Rs þ R0I0DRðtÞ ¼ Rs

Rs þ R0

I0aR0P0

p3=2alDsðtÞ ; ð5Þ

where

DE(t) = DU(t) (1 –– C DU(t))––1 (6)

and

C ¼ 1

RsI0 1 þ gRp

g Rs þ R0ð Þ þ Rp

� � : ð7Þ

The definition of various resistances is found in Fig. 2. Rp is the lead resistance, Rs isa standard resistance with a current rating that is much higher than I0, which is theinitial heating current through the arm of the bridge containing the TPS element, and gis the ratio of the resistances in two ratio arms of the bridge circuit, which is taken tobe 100 in the present case.

3. Material Preparation

High purity (99.999%) Se, Te and Sb in appropriate atomic percentage were weighedinto a quartz glass ampoule of length 5 cm and internal diameter 8 mm. The contents ofthe ampoule (5 g) were sealed into a vacuum of 10––6 Torr (133.2 � 10––6 Pa) and heatedin a furnace, where the temperature was raised at a rate of 3–4 K per min up to 925 Kand kept around that temperature for 7–8 h to ensure the homogeneity of the samples.The molten samples were then rapidly quenched in ice cooled water. Samples obtainedby quenching were in the form of glasses. The glassy state has been confirmed throughX-ray diffraction. These bulk glasses were than crushed to fine powders by a grindingprocess. Pellets of thickness 1 mm and diameter 12 mm were prepared by a pressuremachine at a pressure of 4.33 � 108 Pa.

phys. stat. sol. (a) 189, No. 1 (2002) 199

Fig. 2. Schematic diagram of elec-trical circuit used for simultaneousmeasurements of thermal conduc-tivity and thermal diffusivity

4. Experimental Arrangement

The measurements reported in this paper were performed with a TPS element of thetype shown in Fig. 1. It is made of 10 mm thick nickel foil with an insulating layer madeof 50 mm thick kapton on each side of the metal pattern. Evaluation of these measure-ments was performed in a way that was outlined by Gustafsson [7]. In experiments withinsulating layers of such thickness, it is necessary to ignore the voltage recorded duringthe first few seconds because of the influence of the insulating layers. However, owingto the size of the heated area of the TPS element, the characteristic time of the experi-ment is so long that it is possible to ignore a few seconds of recorded potential differ-ence values and still get very good result.

No influence could be recorded from electrical connections, which are shown inFig. 2. These connecting leads had the same thickness as the metal pattern of the TPSelement. Each TPS element had a resistance at room temperature of about 3.26 W anda TCR of around 4.6 � 10––3 K––1.

An important aspect of the design of any TPS element is that the pattern should besuch that as large a part of the “hot“ area as possible should be covered by the electri-cally conducting pattern, as long as there is insulation between the different parts of thepattern. This is particularly important when insulating layers are covering the conduc-tion pattern and the surface(s) of the sample. It should be noted that the temperaturedifference across the insulating layer can be considered constant after a short initialtransient.

The samples are in the form of pellets of 12 mm diameter and 1 mm thickness, andthe surfaces of these pellets are smooth so as to ensure perfect thermal contact be-tween the samples and the heating elements, as the TPS sensor is sandwiched betweentwo pellets of sample material in the sample holders. The change in voltage was re-corded with a digital voltmeter, which was connected to a personal computer. Thepower output to the sample was adjusted according to the nature of the sample materi-al and was, in most cases, in the range 6–16 � 10––6 W/m2.

5. Result and Discussion

Simultaneous measurements of thermal conductivity and thermal diffusivity ofSe85––xTe15Sbx (x = 2, 4, 6, 8, and 10) glasses, prepared at an ambient pressure of

200 K. Singh et al.: Thermal Conductivity and Diffusivity of Se85––xTe15Sbx Chalcogenide Glasses

Fig. 3. Thermal conductivity vs. anti-mony percentage

4.33 � 108 Pa, have been made at room temperature using the TPS technique. Themeasured values of l and c have been used to obtain the specific heat per unit volume(rcp) as a function of the content x of antimony (Sb), and the results are shown in Figs.3–5, respectively. It can be observed from Figs. 3 and 4 that l and c are maximum at4 at% of Sb for Se–Te–Sb glasses. It has been indicated [10] that in Selenium containingalloys, there is a tendency to form polymerized network glasses and the homopolarbond is qualitatively suppressed. The structure of a Se–Te system prepared by quench-ing is regarded as a mixture of Se8 member rings, Se6Te2 mixed ring and Se–Te chain.A strong covalent bond [11] exists between the atoms in the ring, whereas between thechain only the van der Waals forces are dominant. The l and c increase up to 4 at% ofSb, and with further addition of Sb the chain as well as the ring structures are affected,and as the effects of these on l and c are opposite, both become almost constant athigher atomic percentages of Sb as shown in Figs. 3 and 4. Moreover, at a lower per-centage of Sb the system contains SbSe4/2 tetrahedral units dissolved in a matrix com-posed of Selenium chains. With the increase of Sb content, the glassy matrix becomesheavily crosslinked [12], and the steric hindrance increases. The Se–Se bonds (bondenergy 205.8 kJ/mol) [13] will be replaced by Sb–Se bonds, which have a higher bondenergy (214.2 kJ/mol). Hence the cohesive energy of the system increases with increas-ing Sb content. This results in the increase of l and c. The peak value of l and c is at

4 at% of Sb. This composition canbe considered as a critical composi-tion at which the system can be-come a chemically ordered alloycontaining high energy Sb–Se het-eropolar bonds. Further addition of

phys. stat. sol. (a) 189, No. 1 (2002) 201

Fig. 4. Thermal diffusivity vs. anti-mony percentage

Fig. 5. Specific heat per unit volume vs.antimony percentage

Sb favours the formation of Sb–Sb bonds (bond energy 176.4 kJ/mol), thus reducingthe Sb–Se bond concentration. This in turn results in a decrease of bond energy of(Sb–Sb) –– (Sb–Se) = ––37.8 kJ/mol. Thus the cohesive energy decreases, resulting in adecrease of l and c. It has been noticed that the bond formation energies in the case ofTe–Te and Te–Sb are also small so that the overall structure does not show anychange. The glass transition temperature (Tg), crystallization peak temperature (Tc),their difference (Tc –– Tg), and the glass forming tendency (Kg1) are highest [14] for acomposition of 4 at% Sb, indicating that the glass with 4 at% of Sb is most stable.

The specific heat per unit volume at different compositions is shown in Fig. 5. Fromthe figure it is seen that the minimum specific heat per unit volume is at a compositionwith 4 at% Sb, which is also confirmed through the trend observed for heat released inthe crystallization region of the glass in crystallization kinetic studies [14]. It is due tothe non-availability of a large number of degrees of freedom in the stable alloy, whichcould absorb heat energy, at 4 at% of Sb.

6. Conclusion

Systematic investigation of thermal conductivity and thermal diffusivity of Se–Te–Sbglasses with composition of Sb suggests that at 4 at% of Sb the glass is most thermallystable, which is also confirmed by crystallization kinetics studies.

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202 K. Singh et al.: Thermal Conductivity and Diffusivity of Se85––xTe15Sbx Chalcogenide Glasses