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Int J Thermophys (2014) 35:336–345 DOI 10.1007/s10765-014-1561-0

Effective Thermal-Conductivity Measurement on Germanate Glass–Ceramics Employing the 3ω Method at High Temperature Guo-Ping Su · Lin Qiu · Xing-Hua Zheng · Zhuo-Hao Xiao · Da-Wei Tang

Received: 23 August 2013 / Accepted: 17 January 2014 / Published online: 4 February 2014 © Springer Science+Business Media New York 2014

Abstract It can be noted that the germanate glass–ceramic is a functional material with excellent thermal stability which can be used in optical devices. The temperaturedependent effective thermal conductivities of CaO–BaO–CoO–Al2 O3 –SiO2 –GeO2 glass–ceramics from 295.5 K to 780 K are determined using a 3ω method. One of the main advantages for the 3ω method is to diminish radiation errors effectively when the temperature is as high as 1000 K. Thermal conductivities of CaO–BaO–CoO–Al2 O3 – SiO2 –GeO2 increase with a rise in temperature. Effective thermal conductivities of a sample increase from 1.55 W · m−1 · K−1 at 295.5 K to 7.64 W · m−1 · K−1 at 698.1 K. The effective thermal conductivity of CaO–BaO–CoO–Al2 O3 –SiO2 –GeO2 glass–ceramic increases with a rise of temperature. This investigation can be used as a basis for the measurement of thermal properties of ceramic materials at higher temperature. Keywords 3ω method · Germanate glass–ceramic · High-temperature measurement · Thermal conductivity

G.-P. Su · L. Qiu (B) · X.-H. Zheng (B) · D.-W. Tang Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China e-mail: qiulin@iet.cn X.-H. Zheng e-mail: jzzhengxinghua@163.com G.-P. Su Shenhua Guohua (Beijing) Electric Power Research Institute Co., Ltd., Beijing 100025, China Z.-H. Xiao School of Material Science and China Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China

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1 Introduction Germanate-based glasses belong to one of the heavy metal oxide glasses [1]. They are of great interest because of their excellent optical properties in the mid-wave infrared region (MWIR). Germanate-based glass is an ideal IR window material with outstanding features which include a long IR cutoff wavelength and has had widespread use in many optical components [2,3]. Materials with a weak performance of thermal shock resistance were damaged easily when used in a high-temperature environment. Using a proper heat treatment process to make glass microcrystalline can result in improvement of comprehensive glass performance, such as related to thermal conductivities. Glasses after heat treatment are called glass–ceramics. The heat treatment process and constituents of the germinate glass–ceramic have great effects on its thermal conductivity [4]. It is beneficial to improve their performance of thermal shock resistance through a larger thermal conductivity, because with an increase in the thermal conductivity of a germinate glass–ceramic, the internal thermal stress produced by thermal shock in a glass–ceramic becomes smaller [5]. It makes germinate-based glass more suitable to be used at high temperature. Recently, studies on germanate glass–ceramics have received more attention because of their excellent chemical and thermal stability, simple preparation procedure, easy shaping, excellent performance of thermal shock resistance, and interesting optical properties [6,7]. The temperature dependence of the thermal conductivity and specific heat for germinate glass–ceramics are very helpful to understand and analyze the material [8]. Studies on the thermal properties of glass–ceramic materials have been focused previously on the temperature range from several kelvin to room temperature [9,10]. Zhu and Kosugi [4] measured the thermal conductivities of binary mixed glasses, GeO2 – SiO2 and TiO2 –SiO2 , below 100 K using a conventional steady-state method. The magnitude of the thermal conductivity of GeO2 –SiO2 increases with increasing GeO2 concentration. But at high temperature, the thermal conductivity and specific heat of germinate glass–ceramics have been rarely reported. Generally, thermal properties of bulk materials are determined by steady-state methods, which are used to measure the temperature gradient in one dimension to obtain the thermal conductivity according to Fourier’s law. Heat loss of radiation is much smaller compared with the heat transported near room temperature; hence, errors in measuring the thermal conductivity of bulk materials introduced by the steady-state method are small, and can be acceptable. The thermal conductivity is a vitally important parameter and needs to be determined when glass–ceramics are used at high temperature. However, blackbody radiant heat is proportional to the fourth power of the temperature of the sample and the heat loss increases at higher temperatures. Therefore, this can lead to large errors. The determination of the thermal conductivity by the steady-state method becomes increasing challenging. It is extremely difficult to accurately acquire the thermal properties employing the steady-state technique. These difficulties can be reduced by using the technique which is called the 3ω method [11], in which the blackbody radiant heat loss is decreased by diminishing the sample size. The 3ω method is immune to radiation errors when temperatures are as high as 1000 K. Even at 1000 K, the calculated error due to radiation is less than 2 % [12]. It has other advantages over the steady-state method. For instance, in the 3ω method the testing time is quite short,

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only a few seconds at most, while there are long equilibration times sometimes, even several hours, when using the steady-state method [12]. The laser-flash method can also be used to obtain the thermal diffusion coefficient of bulk materials, from which the thermal conductivity can be deduced. But it is not good for direct measurements on transparent materials. In summary, the 3ω method is a transient measurement technique, which can effectively decrease heat radiation losses, keep the heat flow stable, enhance the measurement speed and accuracy, and is especially suitable for transparent materials. It has been widely used in experimental research on thermal properties of thin films as well as micro- or nano-scale materials [12–15]. The 3ω technique is a promising technique for determining the thermal conductivity of metallic micro-wires and bulk materials below 725 K [11,16]. When the experimental temperature is higher, the contact thermal resistance between the micro-metal prober and the sample is very small and negligible [13]. In recent years, the thermal conductivity and heat conduction mechanisms of glass–ceramics below 1000 K have been paid more and more wide attention. Cahill et al. [17] reported the effect of crystallization on the lattice vibrations of a glass–ceramic through measurements of the thermal conductivity and specific heat below 300 K. The extension of the measurements on ceramics (composition (all in mass%): SiO2 , 56.1 %; Al2 O, 19.8 %; MgO, 14.7 %; etc.) to 700 K was carried out using the 3ω technique. Yang et al. [18] reported measurements of the specific heat and thermal diffusivity of Pyrex 7740 (SiO2 , 80.6 %; B2 O3 , 13 %; Na2 O, 4 %; Al2 O3 , 2.3 %) glass for temperatures between 20 K and 310 K. The thermal conductivity of Pyrex 7740 rises with increasing temperature. For a wide temperature range and short experimental time, the 3ω method is more reliable to precisely determine thermal properties of glass–ceramic materials at high temperature. However, little attention has been devoted to determine the thermal conductivity of germinate glass–ceramics and temperature-dependent thermal conductivity data of these materials remain scarce. In this paper we present results for the effective thermal conductivity and the specific heat of a germinate glass–ceramic (CaO–BaO–CoO–Al2 O3 –SiO2 –GeO2 ). Effective thermal-conductivity values are measured by the 3ω method to cover the temperature range from 295.5 K to 780 K. The maximum temperature of the data measured was limited by the stability of the materials. In addition, we will also discuss the relationship between the holding temperature and effective thermal conductivity of a germinate glass–ceramic. This investigation can be considered as a foundation for utilizing the 3ω method for a broader range of temperature. In order to further explain the mechanism of heat conduction, the specific heat was also measured using a differential scanning calorimeter (DSC 6220).

2 Experimental Details 2.1 Theoretical Basis for the 3ω Method The 3ω method is an ac technique, in which a micro-metal prober with a given size and shape is evaporated onto the surface of a to-be-tested sample; the micro-metal prober is used simultaneously as a heater and thermometer. The thermal properties of the

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bulk material are deduced by the frequency dependence of temperature oscillations [12–15]. The average temperature rise of the metal heater can be obtained from a measurement of the third harmonic of the voltage drop. The relationship between the temperature oscillation and voltage is U3ω =

U1ω αCR T2ω , 2

(1)

where U1ω is the amplitude of the voltage applied across the metal heater, U3ω is the third harmonic of the voltage drop across the metal heater, αCR is the temperature coefficient of resistance (TCR) for the metal heater, αCR = d R/(R0 dT ), and R0 is the metal wire resistance under no heating conditions. Carslaw and Jaeger [19] has acquired the exact solution for the temperature oscillations from an infinitely narrow line source of heat on the surface of an infinite half volume. For the semiinfinite substrate, the approximate solution of metal heater temperature oscillations was achieved by Cahill [12], T2ω = −

π 1 λ P 1 − η + i ln (ω) − ln . lπ λ 2 2 Cb2 4

(2)

In the above expression, b is the metal heater half-width, P/l is the peak electrical power per unit length, λ is the thermal conductivity of the glass–ceramic material, C is the heat capacity, ω is the angular frequency, and η is a constant. In this calculation, we assumed that the metal heater is in intimate thermal contact with the sample. The width of the metal heater, the heat capacity, and the thermal conductivity of the glass– ceramic material are independent of the angular frequency, so we can get the effective thermal conductivity of glass–ceramic materials on the basis of the relationship of the temperature oscillation and frequency. 2.2 Specimen Preparation Three germinate-based glass samples (CaO–BaO–CoO–Al2 O3 –SiO2 –GeO2 ) have the same composition (all in mass%), which are GeO2 , 40–50; SiO2 , 15–25; Al2 O3 , 3–8; CaOBaO, 10–20; CoO, 5–10; else, 1–10. The heat treatment process of three germinate-based glasses is that they are first placed in a high-temperature furnace for 1 h at 1133 K, which is the glass nucleation temperature. Then the set of samples were obtained by holding the temperature at 1203 K, 1223 K, and 1243 K with an isothermal hold of 30 min, respectively, in order to determine the influence of the crystallization temperature on thermal conductivities. The three samples are with different transparencies and show a slight ivory white with an increase in the holding temperature. The thickness of the germinate glass–ceramic samples is larger than 1.8 mm. The length × width (mm × mm) of the three samples are 15.0 × 14.0, 14.5 × 13.6, and 14.8 × 14.0. The germinate glass–ceramic is an insulator, and the surface of the samples is sufficiently smooth. The metal selection for the heaters was primarily based on the resistance-temperature linearity required for the use of the 3ω method. Additionally,

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Fig. 1 Temperature dependence of effective thermal conductivity for AlN ceramics

metal compatibility with available etchants used for mask cleaning was also taken into consideration. In this article, a Ni detector with 200 nm thickness is deposited on the surface of the germinate glass–ceramic to act as a micro-heater. The width of the metal heater is 100 μm. The studied configuration, so-called the four-pad configuration, is described in detail in Refs. [12] and [13]. This geometry leads to a one-dimensional flow of heat in the cross plane direction from which the thermal conductivity can be determined. Once metal heaters have been deposited, wires must be connected to the heater pads. Wire bonding, a technique typically used during the packaging of microelectronic devices, is not required now, because at high temperature (above the fusing point), solder may melt and cannot connect well. Here fine copper wires with a diameter of 0.19 mm are pressed by ceramic plates to connect with the heater pads. The effective thermal properties of three germinate glass–ceramic samples have been investigated from 295.5 K to 780 K. The sample is located in a vacuum chamber. Experiments were carried out in a high-temperature furnace with a vacuum of 0.6 Pa. This vacuum level is low enough to neglect the effect of air conduction, which has been verified by our measurements on an aluminum nitride (AlN) ceramic in the temperature range from room temperature to 1000 K. The results show that the effective thermal conductivity of AlN ceramic from the 3ω method agrees well with that from Watari et al. [20] in the temperature range investigated (shown in Fig. 1), which suggests the measurement system for this vacuum is accurate enough for characterizing the effective thermal conductivity of germanate glass–ceramics. 2.3 Experimental System In the experimental system, the main instruments include: Signal Recovery 7265 lockin amplifier, resistance box, signal generator, circuit integrated equipment, and hightemperature furnace. The electrical current to heat the metal heater is supplied by a signal generator. The amplitude or the real part of the temperature signal is measured

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Fig. 2 Schematic for experiment system using the 3ω method

repeatedly by varying the modulation frequency. For this work, The third harmonic of the voltage drop and the amplitude of the voltage across the metallic heater can be acquired using a DSP lock-in amplifier (Model 7265), which operates over a wide range of frequencies (0.001 Hz to 250 kHz) in conjunction with other instruments shown in Fig. 2. In general, the 3ω signal measured by a lock-in amplifier (7265) is 10−3 to 10−4 times the amplitude of the voltage applied across a micro-heater.

3 Results and Discussion The relationship between the temperature oscillation amplitude and frequency for a micro-heater at 295.5 K is shown in Fig. 3. Then, the behavior of the thermal conductivity with temperature observed in Fig. 4 shows that effective thermal conductivities of germinate glass–ceramic increase with a rise in temperature, which is in agreement with thermal conductivity results for amorphous solids. From 295.5 K to 373 K, effective thermal conductivities of the germinate glass–ceramic increase with a rise in temperature, while it increases slowly in the range from 373 K to 550 K; finally, it increases rapidly above 550 K. Effective thermal conductivities of the No. 1 sample increase from 1.55 W · m−1 · K−1 at 295.5 K to 7.64 W · m−1 · K−1 at 698.1 K. Furthermore, the thermal conductivity changes weakly as a function of temperature and rarely changes by a factor of ten within a general class of material [21]. At 295.5 K, effective thermal conductivities of germinate glass–ceramic are 1.55 W · m−1 · K−1 , 1.93 W · m−1 · K−1 , and 2.58 W · m−1 · K−1 for No. 1, No. 2, and No. 3 samples, respectively, which agree well with the relationship of temperature oscillation amplitudes and frequency for the micro-heater at 295.5 K (Fig. 3). Glass–ceramics are chemically and structurally highly complex solids. Hegab et al. [22] investigated the thermal properties of the Te82.2 Ge13.22 Si4.58 glassy alloy, which is one of the chalcogenide glasses. They showed an increase in thermal conductivity with temperature from 300 K to 350 K. In non-crystalline solids, the thermal conductivity is several orders of magnitude smaller than in crystalline substances [23]. In our work, three germinate glass–ceramic samples are mainly composed of a glass phase with a little crystalline phase. Germanate glass–ceramic samples can be treated as a polycrystal which is composed of extremely fine grains with a diameter of several

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Fig. 3 Temperature oscillation amplitudes versus frequencies for micro-heaters at 295.5 K

Fig. 4 Effective thermal conductivities of germanate glass–ceramic, Pyrex, and α-SiO2 [13] versus temperature

lattice spacings. The transfer of energy in dielectric solids can be regarded as the propagation of anharmonic lattice waves [7]. The thermal conductivity of the germinate glass–ceramic can be described by the phonon heat conduction mechanism, λ=

1 Cvl, 3

(3)

where C is the heat capacity per unit volume, v is the average phonon velocity, and l is the mean free path distance between phonon collisions [18]. The random structure limits the mean free path in glass–ceramics. At high temperatures, the mean free paths for vitreous materials approach the order of a few angstroms, i.e., the inter-atomic separation, as is to be expected [24]. The mean free path is fixed by the structure and is independent of temperature at moderate temperatures. Photon heat conduction can also

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be considered in the samples at high temperature in addition to the phonon thermal conduction. The relationship of the radiation thermal conductivity and temperature is [25] λr =

16 2 3 σ n T lr , 3

(4)

where lr is the radiation photon mean free path, σ is the Stephen–Boltzmann constant (σ = 5.67×10−8 W · m−2 · K−4 ), and n is the refractive index. The radiation thermal conductivity depends mainly on the photon mean free path in the propagation process of radiant energy. The photon mean free path is related with material transparency, and absorption and scattering for the photon with a frequency in the visible light and near-infrared light regions. From 295.5 K to 373 K, the thermal conductivities of germinate glass–ceramic mainly depend on phonon heat conduction. The heat capacity increases with a rise in temperature, and the thermal conductivity of phonons rises at the same time. Heat capacity does not increase any more, and then tends to become a constant with an increase of temperature from 373 K to 550 K. So thermal conductivities caused by phonons are no longer increased, and at this time, photon heat conduction began to increase. Above 550 K, phonon heat conduction has no significant change, but the photon mean free path evidently increased with increasing temperature. According to Eq. 4, photon heat conduction increased rapidly at higher temperatures. Therefore, the thermal conductivity of germinate glass–ceramics (CaO–BaO–CoO–Al2 O3 –SiO2 – GeO2 ) also increases rapidly above 550 K. The above discussion applies to the experimental results in this work. As can be seen in Fig. 4, effective thermal conductivities of the germinate glass–ceramic ascend with a rise of the crystallization temperature, which is from 1203 K, 1223 K to 1243 K. The crystalline phase has been formed in the germinate glass above 1203 K. Furthermore, at higher temperatures, more amorphous phase is crystallized, which leads to bigger effective thermal conductivities of the germinate glass–ceramic. Grains do not expand, but the number of grains becomes larger with an increasing crystallization temperature. Germanate glass–ceramics are still transparent although there are some spots of the crystalline phase [26]. We compared results of this work with thermal conductivities of Pyrex and αSiO2 (Cahill and Pohl [13]), as shown in Fig. 4. The thermal conductivity of pure vitreous GeO2 is higher than that of pure vitreous SiO2 [10]. The effective thermal conductivity of germanate glass–ceramics is higher than Pyrex and α-SiO2 [13]. So, the thermal stability of germanate glass–ceramics is better because of its larger thermal conductivities. And it can be widely used in many applications. In order to further explain the mechanism of heat conduction of germanate glass– ceramics, the specific heat was measured using DSC 6220. Figure 5 illustrates the results of the specific-heat measurements from 303 K to 713 K for No. 1 to No. 3 samples. For the No. 1 sample, a plateau in the curve is observed at about 423 K to 573 K, in which range the effective thermal conductivity changes slowly, while at temperatures above 573 K, the specific heat increases rapidly. For the No. 2 sample, the plateau is still within the above mentioned temperature range, but its increase at

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Fig. 5 Specific heat for No. 1 to No. 3 germanate glass–ceramic samples

temperatures above 573 K is not as obvious as for the No. 1 sample. For the No. 3 sample, the plateau no longer exists and the specific heat keeps increasing above 420 K. This transition from No. 1 to No. 3 samples suggests that for the sample processed at a lower crystallization temperature (No. 1 sample), the amorphous phase become a crystallized phase at the plateau temperature; while for the sample process at elevated temperatures (No. 3 sample), most of the solid phase has crystallized, and the specific heat increases with increasing temperature and no obvious plateau exists. 4 Conclusions In this paper, effective thermal conductivities of a germinate glass–ceramic are measured employing the 3ω method, which increases with temperature from 295.5 K to 780 K. At 295.5 K, effective thermal conductivities of germinate glass–ceramic are 1.55 W · m−1 · K−1 , 1.93 W · m−1 · K−1 , and 2.58 W · m−1 · K−1 for No. 1, No. 2, and No. 3 samples, respectively. In addition, the effective thermal conductivity of the germinate glass–ceramic increases with a rise of the crystallization temperature, which is from 1203 K, 1223 K to 1243 K. To our knowledge, our specific heat and effective thermal-conductivity measurements constitute the first study that covers these two properties in detail for the temperature range between 295.5 K and 780 K. Acknowledgments The authors acknowledge financial support from Project 51306183 supported by National Natural Science Foundation of China and National Basic Research Program of China (Grant No. 2012CB933200). The authors also thank Dr. Zhu Jie for his useful suggestions and interest in this work.

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