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Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity
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JECS-10389; No. of Pages 5
Journal of the European Ceramic Society xxx (2015) xxx–xxx
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Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity David Salamon a,∗ , Radek Kalousek b , Jakub Zlámal b , Karel Maca a a b
CEITEC — Central European Institute of Technology, Brno University of Technology, Technická 3058/10, 61600 Brno, Czech Republic Institute of Physical Engineering and CEITEC BUT, Brno University of Technology, Technická 2, 61600 Brno, Czech Republic
a r t i c l e
i n f o
Article history: Received 29 July 2015 Received in revised form 18 November 2015 Accepted 25 November 2015 Available online xxx Keywords: Rapid sintering Zirconia ceramics Heat transfer Numerical calculation
a b s t r a c t Rapid sintering is nowadays a domain of novel methods such as spark plasma sintering (SPS) or flash sintering. These methods deal with special heating and, therefore, it is difficult to describe obtained results by a conventional pressure-less sintering mechanism. This work deals with specially designed pressureless rapid sintering furnace, which allows heating rates on level of hundreds degrees per minute. Sample with volume over 30 cm3 from low thermally conductive tetragonal zirconia stabilized with 3 mol% Y2 O3 (3Y-TZP) was rapidly sintered to relative density of 86% without crack formation. Experimental data were used for numerical calculations of conduction/convection heat transfer. Obtained results reveal that the maximum temperature in the sample does not exceed 1200 ◦ C if only heating by conduction and convection is considered. Our results indicate that during rapid sintering of low thermally conductive materials radiation heat transfer is dominant in both conventional and SPS conditions. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Rapid pressure-less sintering of ceramics with low thermal conductivity such as tetragonal yttria-stabilized zirconia is usually limited by slow heat transfer. Conventional pressure-less sintering allowed heating rate only 7 ◦ C min−1 during sintering of tetragonal zirconia stabilized with 3 mol% Y2 O3 (3Y-TZP) to prevent crack formation [1]. An alternative rapid sintering technique, hybrid microwave heating allows heating rate of 20 ◦ C min−1 without any observed damage to the 3Y-TZP samples [1]. Faster heating rates during the conventional rapid heating can lead to temperature gradients and, therefore differential densification, low final density, gradient structure, or a specimen crack formation. These difficulties can be overcome by pressure assisted rapid sintering techniques, such as the spark plasma sintering (SPS) method [2] or high-frequency induction heated sintering (HFIHS) [3]. Both techniques permit heating rates up to 200 ◦ C min−1 or even higher without a crack formation of zirconia ceramics, but the applied mechanical pressure during sintering influences a possible crack formation. However, our previous work revealed an unique possibility of sintering crack-free 3Y-TZP ceramics by pressure-less SPS with heating rates up to 500 ◦ C min−1 with no observable grain size
∗ Corresponding author. E-mail address: [email protected] (D. Salamon).
gradients [4]. Presented results seem to be in contradiction with density gradient previously observed during typical fast pressureless sintering of zirconia ceramics, which indicate a requirement of high thermal conductivity for rapid sintering in pressure-less conditions [5]. However, several reports confirmed unique behavior of various materials during pressure-lees SPS. Strong necking of porous materials have been observed for calcium phosphate [6] and silicon nitride [7]. Densification rate comparable with microwave sintering was reported for ZnO2 fine powder [8], but presence of carbon lead to formation of surface patterns as an evidence of surface reaction of ZnO. The term “SPS conditions” includes environment with presence of strong electromagnetic field, low gas pressure (approximately 5 Pa), and presence of carbon. The fast radiation heat transfer is a possible explanation of unique sintering performance of SPS and, therefore, it is desirable to perform rapid sintering in a conventional furnace. However, maximum heating rate in conventional hightemperature furnaces does not allow rapid sintering. Therefore, a modification of the heating process is required to achieve heating rate 100 ◦ C min−1 typical for SPS. Outside SPS furnace there are three possible heat transfer mechanisms conduction/convection and radiation, while generally applied slow heating of zirconia ceramics favors heat conduction/convection. However, the influence of a heat transfer mechanism on rapid sintering of ceramic materials with low thermal conductivity is not clear, and it has main influence on sintering and a crack formation.
http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034 0955-2219/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: D. Salamon, et al., Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity, J Eur Ceram Soc (2015), http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034
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Aim of this work is to inspect the role of conduction and convection heating during rapid sintering of zirconia ceramics in conventional pressure-less conditions. Rapid heating of a large sample (over 30 cm3 ) of 3Y-TZP was performed in especially designed furnace to prove that the crack-free sintering can be performed also under conditions different from SPS. The main difference between the SPS conditions and our design of the experiment consist in the heat transfer by conduction and convection into the sample. Therefore, heating by conduction and convection
was numerically simulated (COMSOL Multiphysics Software) with input data based on experimental results. 2. Experimental Cylindrical zirconia samples were prepared by compaction of green powder of commercially available 3 mol.% Y2 O3 partially stabilized ZrO2 powder (3Y-TZP, average mean particle size 80 nm, Tosoh Co., Tokyo, Japan). Ceramic powder (92 g) was placed in the cylindrical rubber mold and consequently compacted by pressure
Fig. 1. Schematic of the furnace with the moving bottom table used for controlled insertion of the sample into the hot zone. Right down corner: the sample after rapid sintering.
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Fig. 2. SEM microstructure of the 3Y-TZP sample after rapid sintering, (a) core part, (b) rim part.
of 300 MPa by cold isostatic pressing (CIP). Final green compact had its shape close to cylinder with radius 17.5 mm and height 33.0 mm. Organic components of the starting powder were removed by heat treatment at 600 ◦ C for 1 h. The relative density of the green compact (calculated from its dimensions and weight) was 47% compared to 6.08 g cm−3 being the theoretical density (t.d.) of 3Y-TZP. Prepared green body was sintered in a conventional furnace (superkanthal heating elements, air atmosphere) with particularly designed moving sample holder allowing controlled shifting the sample into the hot zone of the furnace, see Fig. 1. Heating regime was set identical with that in SPS [4]: temperature was raised slowly up to 600 ◦ C, from this temperature onward heating rate was increased up to 100 ◦ C min−1 followed by dwell time of 2 min at 1500 ◦ C and cooling at a rate of 100 ◦ C min−1 again. Temperature at a distance 50 mm from the sample was measured by thermocouple during the whole experiment. The temperature development at this point served as input data in the numerical calculations. Density of the sample after sintering was measured by Archimedes method in water. Microstructure of the sintered body was characterized by scanning electron microscope (SEM, Lyra 3 XMH, TESCAN, Czech Republic). Before observation the sintered material was cut horizontally into two halves. The cutting surfaces were polished and thermally etched. The thermal diffusivity of the green compact was measured using the laser flash method (LFA 1000; Linseis, Germany) at room temperature in nitrogen atmosphere. Samples were prepared into pellets of cylindrical shape with diameter 10 mm and height 2–3 mm. Uniaxial pressing of 50 MPa was applied for initial shaping followed by cold isostatic pressing (CIP) of 300 MPa. Two pellets
were prepared at the same pressure to check reproducibility of the powder compaction and its impact on thermal diffusivity. 3. Results Surprisingly, despite the fact that the green-body samples had rather large volume and heating/cooling rates were relatively high, no crack formation was observed on both macro- and micro scale, see inset in Fig. 1 and final microstructure in Fig. 2. Moreover, the sample relative density after sintering was 86% compared to t.d., and no obvious differences between core and rim part were observed, see Fig. 2. To understand how the sample was heated up in such a homogeneous way we simulated the evolution of the temperature field in and near the sample by numerical calculations of both the conduction and convection heat transfer from the heating elements. These calculations were performed within the COMSOL Multiphysics software platform. Since the complete knowledge of the temperature-dependent optical properties of ZrO2 nanopowder in the infrared region was unknown, the contribution from the radiation heat transfer was not taken into account. However, we discuss its role below. The parameters needed to simulate the conduction and convection heat transfer through the air were taken from the COMSOL material library. The quantities describing the conduction heating inside the sample were obtained as follows. The thermal diffusivity ˛ ≡ k/ Cp , where k is the thermal conductivity, Cp is the specific heat capacity, and is the mass density of the material, can be obtained experimentally. The sample is formed by the ZrO2
Fig. 3. (a) Geometry of the numerical calculation: cylindrical sample (green-body diameter 35 mm, height 33 mm) is placed at the center of a box with edge of 250 mm filled with air. (b) Dependence of the temperature on time at the three points A, B, C marked in (a). In the experiment the time development of the local temperature was measured by a thermocouple placed at a distance 50 mm from the sample-point C. The temperature of the heating walls at every instant was set in such a way that the experimental—(violet squares) and simulated (violet curve) developments of the temperature at this point are as close as possible. Simulations were done by COMSOL Multiphysics. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: D. Salamon, et al., Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity, J Eur Ceram Soc (2015), http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034
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Fig. 4. Simulation of the temperature distribution along x axis (see Fig. 3a) at six distinct instants. The temperature at the sample surface reaches its maximum after 13 min, while the maximum temperature in the sample center arrives after 17 min. (b) Map of the temperature field in/near the sample after 17 min. Points A–C correspond to those marked in Fig. 3(a). Simulations were done by COMSOL Multiphysics.
nanoparticles and by an air filling the remaining volume (pores). The fractional density of the sample with respect to the theoretical bulk density of zirconia is also experimentally accessible. Therefore, the thermal conductivity of the sample can be estimated by the following expression:
k∼ = ˛ Cp,ZrO2 ZrO2 + (1 − ) Cp,Air Air .
(1)
Since Cp,ZrO2 ZrO2 >> Cp,Air Air the value of the thermal conductivity of the sample is roughly given by k∼ = ˛Cp,ZrO2 ZrO2 .
(2)
Our calculations were done for the most compacted sample (CIP pressure 300 MPa). The thermal diffusivity ˛ of these samples reached the value of 2.3 × 10−7 m2 s−1 (measured by the laser flash method at 23 ◦ C). The fractional density was close to 0.5 (measured by the Archimedes technique). Since the product of the tabulated values of the specific heat capacity and the mass density for pure zirconia gives Cp,ZrO2 ZrO2 ∼ = 2.3 × 106 J m−3 K−1 , the estimation of the thermal conductivity k of the green-body sample is about 0.26 W m−1 K−1 . Since this value decreases with temperature only slowly, the thermal diffusivity was considered as a constant. The geometry used for the numerical calculation is shown in Fig. 3a. During the experiment the time development of the local temperature was continuously measured by a thermocouple placed at a distance 50 mm from the sample, see Fig. 3a—point C. Therefore, in the numerical calculation the temperature of the heating walls was set in such a way that the experimental and simulated developments of the temperature at this point are as close as possible, see Fig. 3b—curve C. The initial temperature field within all the volume was considered as uniform with the value of 627 ◦ C being the temperature measured by the thermocouple at the beginning of the experiment. The temperature distribution along the x axis at six distinct instants is depicted in Fig. 4a. The temperature field after 17 min, when the temperature in the sample center reaches its maximum, is shown in Fig. 4b. 4. Discussion In this study the sintered sample was 10 time bigger than samples from same powder reported before and no crack formation was observed [5]. The result and heating conditions are similar with rapid sintering performed in non-conventional sintering conditions [4]. This indicates that heat transfer and sintering mechanisms are similar with pressure-less SPS, and change in conduction and convection heat transfer conditions are not critical. One of the widely discussed aspect of SPS is presence of strong electromagnetic field, which may enhance sintering, together with rapid heating rate
[9]. During our experiments strong electromagnetic field was not present, but sintering was still rapid. Numerical calculations demonstrated that the sample cannot be heated up to temperatures higher than 1200 ◦ C only by conduction and convection heat transfer during such a rapid heat treatment lasting only 24 min. Temperatures measured outside temperature profile versus calculated temperature inside the sample are shown in Fig. 3b. The sintering cycle is so fast (heating 100 ◦ C min−1 , dwell 2 min, at 1500 ◦ C) that the sample surface is not heat up to 1200 ◦ C. The conductional and convectional heat transfer is significantly affected by three parameters of heat treatment-heating rate, dwell time, cooling rate. The sample temperature reached by calculation of conductive heating is very low comparing with the level of achieved densification and are not even considered as high enough to reach significant densification and grain growth during pressureless sintering [10]. Thus, considering such a short time, heating only by conduction and convection heat transfer does not correspond to the observed density and microstructure (Fig. 2). Therefore, we are convinced that radiation can represent the decisive heat transfer mechanism during such a rapid sintering of ceramics materials with low thermal conductivity. Generally, zirconia is known as almost transparent material for electromagnetic waves from infrared region at room temperature. Another significant factors influencing the optical properties of the zirconia nanopowder are grain size, green body compaction, temperature, impurities, etc. Therefore, the mechanism how the radiation heat transfer causes such high energy absorption remains unknown and needs to be investigated further. The density of the sintered body was almost homogeneous, only a slight density gradient was observed. However, it is not clear whether the origin of this gradient is caused by the green body density gradient or by the temperature gradient. To make reliable conclusion on this a different method from the cold isostatic pressing should be involved for green body compaction. The presented study of rapid sintering showed slightly different results in case of SPS conditions [4] and the new conventional rapid sintering conditions. However, these variances may have origin in presence of air atmosphere, differently compacted green body, and different temperature measurements (thermocouple vs. pyrometer). Further investigation is necessary to uncover these dissimilarities, but the main character of rapid sintering can be observed also under conditions different from SPS. Comparison of our work with previous studies of fast sintering alternatively to SPS [5] indicates that the rapid sintering has to be fast, preferably hundreds degrees per minute. Heat transfer by radiation is crucial for rapid and homogeneous densification and response of a material to radiation will determine density and microstructure of sintered samples.
5. Conclusions We have shown that crack-free sintering of bulk ceramic material with low thermal conductivity can be achieved by application of rapid sintering in conventional pressure-less conditions. 3Y-TZP sample with volume over 30 cm3 was sintered to 86% of the theoretical density during 24 min without a crack formation. Heat transfer mechanism during the conventional pressure-less rapid sintering was changed, compared with pressure-less SPS, by introducing heat convection, and this change was quantified by numerical calculations. The results demonstrated that conduction and convection heat transfer is not sufficient for sintering during rapid heating of low thermally conductive material such as 3Y-TZP. In this work, we have supported by the experiment and numerical calculation that the heat transfer by radiation represents the key mechanism for the rapid sintering of these materials.
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Acknowledgments This work was supported by grants from Czech Science Foundation (GACR) project no. P108/13-02476S and by the ERDF through project CEITEC (CZ.1.05/1.1.00/02.0068). We thank Ondrej Hanzel for his measurement of thermal diffusivity data and Jakub Roleˇcek for his assistance in preparing of samples. References [1] J. Binner, K. Annapoorani, A. Paul, I. Santacruz, B. Vaidhyanathan, Dense nanostructured zirconia by two stage conventional/hybrid microwave sintering, J. Eur. Ceram. Soc. 28 (2008) 973–977. [2] O. Guillon, J. Gonzalez-Julian, B. Dargatz, T. Kessel, G. Schierning, J. Räthel, et al., Field-assisted sintering technology/spark plasma sintering: mechanisms, materials, and technology developments, Adv. Eng. Mater. 16 (2014) 830–849. [3] H.-C. Kim, I.-J. Shon, I.-K. Jeong, I.-Y. Ko, Z.A. Munir, Sintering of ultra-fine tetragonal yttria-stabilized zirconia ceramics, J. Mater. Sci. 42 (2007) 9409–9414.
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[4] D. Salamon, K. Maca, Z. Shen, Rapid sintering of crack-free zirconia ceramics by pressure-less spark plasma sintering, Scr. Mater. 66 (2012) 899–902. [5] M.J. Mayo, Processing of nanocrystalline ceramics from ultrafine particles, Int. Mater. Rev. 41 (1996) 85–115. [6] F. Zhang, K. Lin, J. Chang, J. Lu, C. Ning, Spark plasma sintering of macroporous calcium phosphate scaffolds from nanocrystalline powders, J. Eur. Ceram. Soc. 28 (2008) 539–545. [7] D. Li, E. Guzi de Moraes, P. Guo, J. Zou, J. Zhang, P. Colombo, et al., Rapid sintering of silicon nitride foams decorated with one-dimensional nanostructures by intense thermal radiation, Sci. Technol. Adv. Mater. 15 (2014), 045003. [8] R. Yamano˘glu, W.L. Bradbury, E.A. Olevsky, R.M. German, Comparative evaluation of densification and grain size of ZnO powder compacts during microwave and pressureless spark plasma sintering, Adv. Appl. Ceram. 111 (2012) 422–426. [9] R. Chaim, Electric field effects during spark plasma sintering of ceramic nanoparticles, J. Mater. Sci. 48 (2012) 502–510. [10] R. Chaim, Activation energy and grain growth in nanocrystalline Y-TZP ceramics, Mater. Sci. Eng. A 486 (2008) 439–446.
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Contents lists available at www.sciencedirect.com
Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc
Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity David Salamon a,∗ , Radek Kalousek b , Jakub Zlámal b , Karel Maca a a b
CEITEC — Central European Institute of Technology, Brno University of Technology, Technická 3058/10, 61600 Brno, Czech Republic Institute of Physical Engineering and CEITEC BUT, Brno University of Technology, Technická 2, 61600 Brno, Czech Republic
a r t i c l e
i n f o
Article history: Received 29 July 2015 Received in revised form 18 November 2015 Accepted 25 November 2015 Available online xxx Keywords: Rapid sintering Zirconia ceramics Heat transfer Numerical calculation
a b s t r a c t Rapid sintering is nowadays a domain of novel methods such as spark plasma sintering (SPS) or flash sintering. These methods deal with special heating and, therefore, it is difficult to describe obtained results by a conventional pressure-less sintering mechanism. This work deals with specially designed pressureless rapid sintering furnace, which allows heating rates on level of hundreds degrees per minute. Sample with volume over 30 cm3 from low thermally conductive tetragonal zirconia stabilized with 3 mol% Y2 O3 (3Y-TZP) was rapidly sintered to relative density of 86% without crack formation. Experimental data were used for numerical calculations of conduction/convection heat transfer. Obtained results reveal that the maximum temperature in the sample does not exceed 1200 ◦ C if only heating by conduction and convection is considered. Our results indicate that during rapid sintering of low thermally conductive materials radiation heat transfer is dominant in both conventional and SPS conditions. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Rapid pressure-less sintering of ceramics with low thermal conductivity such as tetragonal yttria-stabilized zirconia is usually limited by slow heat transfer. Conventional pressure-less sintering allowed heating rate only 7 ◦ C min−1 during sintering of tetragonal zirconia stabilized with 3 mol% Y2 O3 (3Y-TZP) to prevent crack formation [1]. An alternative rapid sintering technique, hybrid microwave heating allows heating rate of 20 ◦ C min−1 without any observed damage to the 3Y-TZP samples [1]. Faster heating rates during the conventional rapid heating can lead to temperature gradients and, therefore differential densification, low final density, gradient structure, or a specimen crack formation. These difficulties can be overcome by pressure assisted rapid sintering techniques, such as the spark plasma sintering (SPS) method [2] or high-frequency induction heated sintering (HFIHS) [3]. Both techniques permit heating rates up to 200 ◦ C min−1 or even higher without a crack formation of zirconia ceramics, but the applied mechanical pressure during sintering influences a possible crack formation. However, our previous work revealed an unique possibility of sintering crack-free 3Y-TZP ceramics by pressure-less SPS with heating rates up to 500 ◦ C min−1 with no observable grain size
∗ Corresponding author. E-mail address: [email protected] (D. Salamon).
gradients [4]. Presented results seem to be in contradiction with density gradient previously observed during typical fast pressureless sintering of zirconia ceramics, which indicate a requirement of high thermal conductivity for rapid sintering in pressure-less conditions [5]. However, several reports confirmed unique behavior of various materials during pressure-lees SPS. Strong necking of porous materials have been observed for calcium phosphate [6] and silicon nitride [7]. Densification rate comparable with microwave sintering was reported for ZnO2 fine powder [8], but presence of carbon lead to formation of surface patterns as an evidence of surface reaction of ZnO. The term “SPS conditions” includes environment with presence of strong electromagnetic field, low gas pressure (approximately 5 Pa), and presence of carbon. The fast radiation heat transfer is a possible explanation of unique sintering performance of SPS and, therefore, it is desirable to perform rapid sintering in a conventional furnace. However, maximum heating rate in conventional hightemperature furnaces does not allow rapid sintering. Therefore, a modification of the heating process is required to achieve heating rate 100 ◦ C min−1 typical for SPS. Outside SPS furnace there are three possible heat transfer mechanisms conduction/convection and radiation, while generally applied slow heating of zirconia ceramics favors heat conduction/convection. However, the influence of a heat transfer mechanism on rapid sintering of ceramic materials with low thermal conductivity is not clear, and it has main influence on sintering and a crack formation.
http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034 0955-2219/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: D. Salamon, et al., Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity, J Eur Ceram Soc (2015), http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034
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Aim of this work is to inspect the role of conduction and convection heating during rapid sintering of zirconia ceramics in conventional pressure-less conditions. Rapid heating of a large sample (over 30 cm3 ) of 3Y-TZP was performed in especially designed furnace to prove that the crack-free sintering can be performed also under conditions different from SPS. The main difference between the SPS conditions and our design of the experiment consist in the heat transfer by conduction and convection into the sample. Therefore, heating by conduction and convection
was numerically simulated (COMSOL Multiphysics Software) with input data based on experimental results. 2. Experimental Cylindrical zirconia samples were prepared by compaction of green powder of commercially available 3 mol.% Y2 O3 partially stabilized ZrO2 powder (3Y-TZP, average mean particle size 80 nm, Tosoh Co., Tokyo, Japan). Ceramic powder (92 g) was placed in the cylindrical rubber mold and consequently compacted by pressure
Fig. 1. Schematic of the furnace with the moving bottom table used for controlled insertion of the sample into the hot zone. Right down corner: the sample after rapid sintering.
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Fig. 2. SEM microstructure of the 3Y-TZP sample after rapid sintering, (a) core part, (b) rim part.
of 300 MPa by cold isostatic pressing (CIP). Final green compact had its shape close to cylinder with radius 17.5 mm and height 33.0 mm. Organic components of the starting powder were removed by heat treatment at 600 ◦ C for 1 h. The relative density of the green compact (calculated from its dimensions and weight) was 47% compared to 6.08 g cm−3 being the theoretical density (t.d.) of 3Y-TZP. Prepared green body was sintered in a conventional furnace (superkanthal heating elements, air atmosphere) with particularly designed moving sample holder allowing controlled shifting the sample into the hot zone of the furnace, see Fig. 1. Heating regime was set identical with that in SPS [4]: temperature was raised slowly up to 600 ◦ C, from this temperature onward heating rate was increased up to 100 ◦ C min−1 followed by dwell time of 2 min at 1500 ◦ C and cooling at a rate of 100 ◦ C min−1 again. Temperature at a distance 50 mm from the sample was measured by thermocouple during the whole experiment. The temperature development at this point served as input data in the numerical calculations. Density of the sample after sintering was measured by Archimedes method in water. Microstructure of the sintered body was characterized by scanning electron microscope (SEM, Lyra 3 XMH, TESCAN, Czech Republic). Before observation the sintered material was cut horizontally into two halves. The cutting surfaces were polished and thermally etched. The thermal diffusivity of the green compact was measured using the laser flash method (LFA 1000; Linseis, Germany) at room temperature in nitrogen atmosphere. Samples were prepared into pellets of cylindrical shape with diameter 10 mm and height 2–3 mm. Uniaxial pressing of 50 MPa was applied for initial shaping followed by cold isostatic pressing (CIP) of 300 MPa. Two pellets
were prepared at the same pressure to check reproducibility of the powder compaction and its impact on thermal diffusivity. 3. Results Surprisingly, despite the fact that the green-body samples had rather large volume and heating/cooling rates were relatively high, no crack formation was observed on both macro- and micro scale, see inset in Fig. 1 and final microstructure in Fig. 2. Moreover, the sample relative density after sintering was 86% compared to t.d., and no obvious differences between core and rim part were observed, see Fig. 2. To understand how the sample was heated up in such a homogeneous way we simulated the evolution of the temperature field in and near the sample by numerical calculations of both the conduction and convection heat transfer from the heating elements. These calculations were performed within the COMSOL Multiphysics software platform. Since the complete knowledge of the temperature-dependent optical properties of ZrO2 nanopowder in the infrared region was unknown, the contribution from the radiation heat transfer was not taken into account. However, we discuss its role below. The parameters needed to simulate the conduction and convection heat transfer through the air were taken from the COMSOL material library. The quantities describing the conduction heating inside the sample were obtained as follows. The thermal diffusivity ˛ ≡ k/ Cp , where k is the thermal conductivity, Cp is the specific heat capacity, and is the mass density of the material, can be obtained experimentally. The sample is formed by the ZrO2
Fig. 3. (a) Geometry of the numerical calculation: cylindrical sample (green-body diameter 35 mm, height 33 mm) is placed at the center of a box with edge of 250 mm filled with air. (b) Dependence of the temperature on time at the three points A, B, C marked in (a). In the experiment the time development of the local temperature was measured by a thermocouple placed at a distance 50 mm from the sample-point C. The temperature of the heating walls at every instant was set in such a way that the experimental—(violet squares) and simulated (violet curve) developments of the temperature at this point are as close as possible. Simulations were done by COMSOL Multiphysics. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: D. Salamon, et al., Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity, J Eur Ceram Soc (2015), http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034
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Fig. 4. Simulation of the temperature distribution along x axis (see Fig. 3a) at six distinct instants. The temperature at the sample surface reaches its maximum after 13 min, while the maximum temperature in the sample center arrives after 17 min. (b) Map of the temperature field in/near the sample after 17 min. Points A–C correspond to those marked in Fig. 3(a). Simulations were done by COMSOL Multiphysics.
nanoparticles and by an air filling the remaining volume (pores). The fractional density of the sample with respect to the theoretical bulk density of zirconia is also experimentally accessible. Therefore, the thermal conductivity of the sample can be estimated by the following expression:
k∼ = ˛ Cp,ZrO2 ZrO2 + (1 − ) Cp,Air Air .
(1)
Since Cp,ZrO2 ZrO2 >> Cp,Air Air the value of the thermal conductivity of the sample is roughly given by k∼ = ˛Cp,ZrO2 ZrO2 .
(2)
Our calculations were done for the most compacted sample (CIP pressure 300 MPa). The thermal diffusivity ˛ of these samples reached the value of 2.3 × 10−7 m2 s−1 (measured by the laser flash method at 23 ◦ C). The fractional density was close to 0.5 (measured by the Archimedes technique). Since the product of the tabulated values of the specific heat capacity and the mass density for pure zirconia gives Cp,ZrO2 ZrO2 ∼ = 2.3 × 106 J m−3 K−1 , the estimation of the thermal conductivity k of the green-body sample is about 0.26 W m−1 K−1 . Since this value decreases with temperature only slowly, the thermal diffusivity was considered as a constant. The geometry used for the numerical calculation is shown in Fig. 3a. During the experiment the time development of the local temperature was continuously measured by a thermocouple placed at a distance 50 mm from the sample, see Fig. 3a—point C. Therefore, in the numerical calculation the temperature of the heating walls was set in such a way that the experimental and simulated developments of the temperature at this point are as close as possible, see Fig. 3b—curve C. The initial temperature field within all the volume was considered as uniform with the value of 627 ◦ C being the temperature measured by the thermocouple at the beginning of the experiment. The temperature distribution along the x axis at six distinct instants is depicted in Fig. 4a. The temperature field after 17 min, when the temperature in the sample center reaches its maximum, is shown in Fig. 4b. 4. Discussion In this study the sintered sample was 10 time bigger than samples from same powder reported before and no crack formation was observed [5]. The result and heating conditions are similar with rapid sintering performed in non-conventional sintering conditions [4]. This indicates that heat transfer and sintering mechanisms are similar with pressure-less SPS, and change in conduction and convection heat transfer conditions are not critical. One of the widely discussed aspect of SPS is presence of strong electromagnetic field, which may enhance sintering, together with rapid heating rate
[9]. During our experiments strong electromagnetic field was not present, but sintering was still rapid. Numerical calculations demonstrated that the sample cannot be heated up to temperatures higher than 1200 ◦ C only by conduction and convection heat transfer during such a rapid heat treatment lasting only 24 min. Temperatures measured outside temperature profile versus calculated temperature inside the sample are shown in Fig. 3b. The sintering cycle is so fast (heating 100 ◦ C min−1 , dwell 2 min, at 1500 ◦ C) that the sample surface is not heat up to 1200 ◦ C. The conductional and convectional heat transfer is significantly affected by three parameters of heat treatment-heating rate, dwell time, cooling rate. The sample temperature reached by calculation of conductive heating is very low comparing with the level of achieved densification and are not even considered as high enough to reach significant densification and grain growth during pressureless sintering [10]. Thus, considering such a short time, heating only by conduction and convection heat transfer does not correspond to the observed density and microstructure (Fig. 2). Therefore, we are convinced that radiation can represent the decisive heat transfer mechanism during such a rapid sintering of ceramics materials with low thermal conductivity. Generally, zirconia is known as almost transparent material for electromagnetic waves from infrared region at room temperature. Another significant factors influencing the optical properties of the zirconia nanopowder are grain size, green body compaction, temperature, impurities, etc. Therefore, the mechanism how the radiation heat transfer causes such high energy absorption remains unknown and needs to be investigated further. The density of the sintered body was almost homogeneous, only a slight density gradient was observed. However, it is not clear whether the origin of this gradient is caused by the green body density gradient or by the temperature gradient. To make reliable conclusion on this a different method from the cold isostatic pressing should be involved for green body compaction. The presented study of rapid sintering showed slightly different results in case of SPS conditions [4] and the new conventional rapid sintering conditions. However, these variances may have origin in presence of air atmosphere, differently compacted green body, and different temperature measurements (thermocouple vs. pyrometer). Further investigation is necessary to uncover these dissimilarities, but the main character of rapid sintering can be observed also under conditions different from SPS. Comparison of our work with previous studies of fast sintering alternatively to SPS [5] indicates that the rapid sintering has to be fast, preferably hundreds degrees per minute. Heat transfer by radiation is crucial for rapid and homogeneous densification and response of a material to radiation will determine density and microstructure of sintered samples.
5. Conclusions We have shown that crack-free sintering of bulk ceramic material with low thermal conductivity can be achieved by application of rapid sintering in conventional pressure-less conditions. 3Y-TZP sample with volume over 30 cm3 was sintered to 86% of the theoretical density during 24 min without a crack formation. Heat transfer mechanism during the conventional pressure-less rapid sintering was changed, compared with pressure-less SPS, by introducing heat convection, and this change was quantified by numerical calculations. The results demonstrated that conduction and convection heat transfer is not sufficient for sintering during rapid heating of low thermally conductive material such as 3Y-TZP. In this work, we have supported by the experiment and numerical calculation that the heat transfer by radiation represents the key mechanism for the rapid sintering of these materials.
Please cite this article in press as: D. Salamon, et al., Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity, J Eur Ceram Soc (2015), http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034
G Model JECS-10389; No. of Pages 5
ARTICLE IN PRESS D. Salamon et al. / Journal of the European Ceramic Society xxx (2015) xxx–xxx
Acknowledgments This work was supported by grants from Czech Science Foundation (GACR) project no. P108/13-02476S and by the ERDF through project CEITEC (CZ.1.05/1.1.00/02.0068). We thank Ondrej Hanzel for his measurement of thermal diffusivity data and Jakub Roleˇcek for his assistance in preparing of samples. References [1] J. Binner, K. Annapoorani, A. Paul, I. Santacruz, B. Vaidhyanathan, Dense nanostructured zirconia by two stage conventional/hybrid microwave sintering, J. Eur. Ceram. Soc. 28 (2008) 973–977. [2] O. Guillon, J. Gonzalez-Julian, B. Dargatz, T. Kessel, G. Schierning, J. Räthel, et al., Field-assisted sintering technology/spark plasma sintering: mechanisms, materials, and technology developments, Adv. Eng. Mater. 16 (2014) 830–849. [3] H.-C. Kim, I.-J. Shon, I.-K. Jeong, I.-Y. Ko, Z.A. Munir, Sintering of ultra-fine tetragonal yttria-stabilized zirconia ceramics, J. Mater. Sci. 42 (2007) 9409–9414.
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Please cite this article in press as: D. Salamon, et al., Role of conduction and convection heat transfer during rapid crack-free sintering of bulk ceramic with low thermal conductivity, J Eur Ceram Soc (2015), http://dx.doi.org/10.1016/j.jeurceramsoc.2015.11.034