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Thermal diffusivity of pure and impurity-doped titanium dioxides ceramics
Journal of Materials Processing Technology 113 (2001) 474±476
Thermal diffusivity of pure and impurity-doped titanium dioxides ceramics X. Fanga, P. Hinga, J.T. Oha,*, H.S. Fonga, X. Chenb, M. Wub a
Advanced Materials Research Centre, School of Materials Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore b School of Science, Xian Jiaotong University, Xian City, PR China
Abstract The thermal diffusivity of pure and Sn-, Nb-, Ta-, and W-doped titanium dioxide ceramics had been investigated at different temperatures. Most of the results could be interpreted in terms of phonon scattering by vacancy or impurity. The thermal diffusivity behavior of Nb- and W-doped titanium oxide shows that the electronic transition contributes to the thermal diffusivity. Ta-doped titanium dioxide ceramics exhibit an increase in thermal diffusivity with temperature. A possible explanation for the unusual behavior in the thermal diffusivity is presented and discussed. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Thermal diffusivity; Titanium dioxides; Ceramics
1. Introduction Titanium dioxide is used widely as a functional electronic material for applications in devices such as varistors, capacitors, and gas and humidity sensors. In addition, reduced and doped TiO2 behaves as a semiconductor due to the introduction of impurity energy levels in the energy band structure. Previous studies on the processing of these applications has mainly focussed on the electrical and dielectric properties. However, only limited reports are available on thermal physical characteristics of the reduced and doped TiO2. The objectives of this study are to investigate the thermal physical properties of doped and semi-conducting titanium dioxide, and to evaluate its applicability as thermally and electrically conducting materials. 2. Theory The lattice contribution to thermal conductivity, k, is given by Kittel [1]: k 13 cp v l
(1)
limited through cp by the Debye T3 law. For impure crystals, l is limited by the phonon±impurity interactions. The scattering cross-section, G, for the scattering of phonons by impurity atoms is given by Abeles [2] and Slack [3]: " 2 # DM 2 Dd G Xs 1 Xs e (2) M d where DM/M and Dd/d are the mass and strain mis®ts, respectively, e is a dimensionless parameter, and Xs is the concentration of the solute. For intermediate temperature range with strong phonon-defect scattering, the thermal conductivity, k, is 1 k p A GT BT
(3)
where A and B are constants that are independent of the p temperature. At intermediate temperature, GT @ BT and k / T 0:5 . Hence the thermal conductivity, k, is dependent primarily on the scattering cross-section, G, which in turn is dependent on the volume concentration of the impurity and the mass and strain mis®ts (Eq. (2)).
where cp is the speci®c heat capacity, v the phonon velocity and l the phonon mean free path. At low temperatures, k is
3. Experimental procedure
* Corresponding author. E-mail address: [email protected] (O.J. Tien).
Pure and Sn-, Nb-, Ta-, and W-doped TiO2 ceramic samples were prepared with Analar Grade TiO2, SnO2,
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 5 9 8 - 2
F. Xiangyi et al. / Journal of Materials Processing Technology 113 (2001) 474±476
Nb2O5, Ta2O5, and WO3 powders. The powders were ball milled with ZrO2 media in distilled water for 24 h to obtain a uniform distribution of the oxide additive in TiO2 and also to reduce the particle size of the starting materials. The slurry was then dried at 1008C for 8 h. The dried powders were then pressed by double-acting compaction into disks of 12mm diameter and 2±3-mm thickness. The Sn-, Nb-, Ta-, and W-doped TiO2 ceramics were sintered in air at different temperatures. The reduced TiO2 was prepared by hot isostatic pressing (HIP) and also by use of a belt furnace in argon gas. The crystal structure of the samples was determined using XRD using Cu Ka radiation while the thermal diffusivity was measured using the laser ¯ash method Netzsch LFA-427 model. 4. Results and discussion 4.1. XRD results Fig. 1 shows the XRD patterns of the samples. Both the doped and reduced samples exhibit a rutile structure. Reduced phases Tin O2n 1 such as n 3; 4; 5; 6; 7; 8; 9 were not found. It should be noted that new peaks at about 37.668 and 37.588 for 0.6 mol% of Nb2O5 and 1.0 mol% of Ta2O5 doped samples, respectively, were observed. Nevertheless, the color change clearly suggests that reduction of TiO2 has occurred. The samples show a uniform black color. The electrical resistance at room temperature is 2 O cm. The high electrical conductivity and color change are attributed to the defects formed by oxygen de®ciency. 4.2. Thermal diffusivity Fig. 2 shows the thermal diffusivity of the reduced TiO2 and Sn-doped samples sintered in argon and air, respectively. The reduced TiO2 and the Sn-doped sample sintered in air
Fig. 1. XRD patterns of reduced and doped TiO2. (A) TiO2 sintered in air; (B) TiO2 sintered in argon; (C) TiO2 doped with 0.5 mol% of Nb2O5 and sintered in air; (D) TiO2 doped with 0.7 mol% of Nb2O5 and sintered in air; (E) TiO2 doped with 1.0 mol% of Ta2O5 and sintered in air; (F) TiO2 doped with 0.6 mol% of Ta2O5 and sintered in air; (G) TiO2 doped with 0.4 mol% of WO3 and sintered in air; (H) TiO2 doped with 0.6 mol% of WO3 and sintered in air.
475
Fig. 2. Thermal diffusivity of pure and Sn-doped TiO2. (A) sintered in air; (B) Sn-doped and sintered in air; (C) sintered in argon belt furnace (reduced TiO2).
have a lower thermal diffusivity than that of pure TiO2 sintered in air. These results are consistent with the phonon scattering theory [1], i.e. scattering of the phonons by vacancy and doped impurities. Fig. 3 shows the thermal diffusivity of Nb-doped TiO2 sintered in air. With the incorporation of 0.5 mol% of Nb2O5, the thermal diffusivity is lower than that of pure TiO2 and shows a steady reduction with temperature. This trend is similar to that of pure TiO2. This could be attributed to Nb impurities acting as the phonon scatterer. In view of the fact that the addition of 0.5 mol% of Nb2O5, will result in the material being semi-conducting [4,5] with electronics transition, it did not seem to contribute to heat conduction above 2008C. However, when 0.7 mol% of Nb2O5 was added, the thermal diffusivity is signi®cantly higher than that with 0.5 mol% of Nb2O5. Below 1508C, the decay of thermal diffusivity versus temperature graph suggests that the dominant contribution to the thermal diffusivity is due to phonon transition. Above 1508C, the thermal diffusivity increases with temperature. This is inconsistent with the phonon scattering theory and hence it is reasonable to conclude that there is another mechanism of thermal diffusivity beside the phonon transition. It is reasonable to conclude that the electronics transition should be taken into account here.
Fig. 3. Thermal diffusivity of Nb-doped and pure TiO2 sintered in air.
476
F. Xiangyi et al. / Journal of Materials Processing Technology 113 (2001) 474±476
effect of electronic transition has a more pronounced effect than that of phonon scattering. 5. Conclusions
Fig. 4. Thermal diffusivity of Ta-doped and pure TiO2.
Fig. 5. Thermal diffusivity of W-doped TiO2.
Fig. 4 shows the thermal diffusivity of Ta-doped TiO2 versus temperature. Compared with Nb-doped samples, Ta doping had not resulted in any reduction of thermal diffusivity. This is contrary to the phonon scattering theory because Eqs. (2) and (3) showed that doping with elements of differing atomic radii would result in mass and strain mis®ts. The resulting mass and strain mis®ts will in theory increase the scattering cross-section, hence reducing the thermal conductivity. Thus, it is suspected that the addition of the Ta impurities that caused the samples to be semiconducting has also resulted in increasing the thermal diffusivity of the material. The thermal diffusivity of W-doped titanium dioxide is shown in Fig. 5. The thermal diffusivities of the doped samples are consistently higher than those of the pure samples for all temperatures and compositions. A peak near 2008C instead of decaying with temperature shows that the
The thermal diffusivity of processed titanium dioxide by reduction and doping with Sn, Nb, W, Ta has been measured. The reduced and Sn-doped TiO2 exhibit a monotonic decay of thermal diffusivity and are consistent with the feature of phonon scattering by vacancy and doped impurities. The thermal diffusivity of Nb-doped TiO2 shows different characteristics with different amount of additives. When the doping amount of Nb is 0.7 mol%, the thermal diffusivity above 1508C tends to increase. This behavior could not be explained only by the phonon scatter theory. A more probable explanation is that the addition of 0.7 mol% of Nb has introduced impurity energy levels in the energy band structure, thus rendering it semi-conducting. Hence an associated increase in thermal conductivity is observed. All the Tadoped samples show monotonic decay of thermal diffusivity but the diffusivity of these samples is still higher than what of pure TiO2. This implies that the doped Ta impurities are not strong phonon scatterers. W doping resulted in a peak in the thermal diffusivity. Acknowledgements This work is supported by the Tan Chin Tuan Fellowship from Nanyang Technological University, Singapore. The assistance of Mr. Huang Haitao, Mrs. Zahara Ahmad and Mrs. Sory is gratefully acknowledged. References [1] C. Kittel, Introduction to Solid-state Physics, 3rd Edition, Wiley, New York, 1967. [2] B. Abeles, Lattice thermal conductivity of disordered semiconductors at high temperatures, Phys. Rev. 131 (5) (1963) 1906±1911. [3] G.A. Slack, Thermal conductivity of MgO, Al2O3, MgAl2O4 and Fe3O4 crystals from 3 to 300 K, Phys. Rev. 126 (2) (1962) 427±441. [4] F. Xiangyi, et al., Semiconducting TiO2 ceramics, J. Mater. Sci. 7 (3) (1993) 245±247 (in Chinese). [5] F. Xiangyi, et al., Research on TiO2 thick ®lm for oxygen sensor, J. Yun Nan Univ. 19 (2) (1997) 135±138 (in Chinese).
Thermal diffusivity of pure and impurity-doped titanium dioxides ceramics X. Fanga, P. Hinga, J.T. Oha,*, H.S. Fonga, X. Chenb, M. Wub a
Advanced Materials Research Centre, School of Materials Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore b School of Science, Xian Jiaotong University, Xian City, PR China
Abstract The thermal diffusivity of pure and Sn-, Nb-, Ta-, and W-doped titanium dioxide ceramics had been investigated at different temperatures. Most of the results could be interpreted in terms of phonon scattering by vacancy or impurity. The thermal diffusivity behavior of Nb- and W-doped titanium oxide shows that the electronic transition contributes to the thermal diffusivity. Ta-doped titanium dioxide ceramics exhibit an increase in thermal diffusivity with temperature. A possible explanation for the unusual behavior in the thermal diffusivity is presented and discussed. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Thermal diffusivity; Titanium dioxides; Ceramics
1. Introduction Titanium dioxide is used widely as a functional electronic material for applications in devices such as varistors, capacitors, and gas and humidity sensors. In addition, reduced and doped TiO2 behaves as a semiconductor due to the introduction of impurity energy levels in the energy band structure. Previous studies on the processing of these applications has mainly focussed on the electrical and dielectric properties. However, only limited reports are available on thermal physical characteristics of the reduced and doped TiO2. The objectives of this study are to investigate the thermal physical properties of doped and semi-conducting titanium dioxide, and to evaluate its applicability as thermally and electrically conducting materials. 2. Theory The lattice contribution to thermal conductivity, k, is given by Kittel [1]: k 13 cp v l
(1)
limited through cp by the Debye T3 law. For impure crystals, l is limited by the phonon±impurity interactions. The scattering cross-section, G, for the scattering of phonons by impurity atoms is given by Abeles [2] and Slack [3]: " 2 # DM 2 Dd G Xs 1 Xs e (2) M d where DM/M and Dd/d are the mass and strain mis®ts, respectively, e is a dimensionless parameter, and Xs is the concentration of the solute. For intermediate temperature range with strong phonon-defect scattering, the thermal conductivity, k, is 1 k p A GT BT
(3)
where A and B are constants that are independent of the p temperature. At intermediate temperature, GT @ BT and k / T 0:5 . Hence the thermal conductivity, k, is dependent primarily on the scattering cross-section, G, which in turn is dependent on the volume concentration of the impurity and the mass and strain mis®ts (Eq. (2)).
where cp is the speci®c heat capacity, v the phonon velocity and l the phonon mean free path. At low temperatures, k is
3. Experimental procedure
* Corresponding author. E-mail address: [email protected] (O.J. Tien).
Pure and Sn-, Nb-, Ta-, and W-doped TiO2 ceramic samples were prepared with Analar Grade TiO2, SnO2,
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 5 9 8 - 2
F. Xiangyi et al. / Journal of Materials Processing Technology 113 (2001) 474±476
Nb2O5, Ta2O5, and WO3 powders. The powders were ball milled with ZrO2 media in distilled water for 24 h to obtain a uniform distribution of the oxide additive in TiO2 and also to reduce the particle size of the starting materials. The slurry was then dried at 1008C for 8 h. The dried powders were then pressed by double-acting compaction into disks of 12mm diameter and 2±3-mm thickness. The Sn-, Nb-, Ta-, and W-doped TiO2 ceramics were sintered in air at different temperatures. The reduced TiO2 was prepared by hot isostatic pressing (HIP) and also by use of a belt furnace in argon gas. The crystal structure of the samples was determined using XRD using Cu Ka radiation while the thermal diffusivity was measured using the laser ¯ash method Netzsch LFA-427 model. 4. Results and discussion 4.1. XRD results Fig. 1 shows the XRD patterns of the samples. Both the doped and reduced samples exhibit a rutile structure. Reduced phases Tin O2n 1 such as n 3; 4; 5; 6; 7; 8; 9 were not found. It should be noted that new peaks at about 37.668 and 37.588 for 0.6 mol% of Nb2O5 and 1.0 mol% of Ta2O5 doped samples, respectively, were observed. Nevertheless, the color change clearly suggests that reduction of TiO2 has occurred. The samples show a uniform black color. The electrical resistance at room temperature is 2 O cm. The high electrical conductivity and color change are attributed to the defects formed by oxygen de®ciency. 4.2. Thermal diffusivity Fig. 2 shows the thermal diffusivity of the reduced TiO2 and Sn-doped samples sintered in argon and air, respectively. The reduced TiO2 and the Sn-doped sample sintered in air
Fig. 1. XRD patterns of reduced and doped TiO2. (A) TiO2 sintered in air; (B) TiO2 sintered in argon; (C) TiO2 doped with 0.5 mol% of Nb2O5 and sintered in air; (D) TiO2 doped with 0.7 mol% of Nb2O5 and sintered in air; (E) TiO2 doped with 1.0 mol% of Ta2O5 and sintered in air; (F) TiO2 doped with 0.6 mol% of Ta2O5 and sintered in air; (G) TiO2 doped with 0.4 mol% of WO3 and sintered in air; (H) TiO2 doped with 0.6 mol% of WO3 and sintered in air.
475
Fig. 2. Thermal diffusivity of pure and Sn-doped TiO2. (A) sintered in air; (B) Sn-doped and sintered in air; (C) sintered in argon belt furnace (reduced TiO2).
have a lower thermal diffusivity than that of pure TiO2 sintered in air. These results are consistent with the phonon scattering theory [1], i.e. scattering of the phonons by vacancy and doped impurities. Fig. 3 shows the thermal diffusivity of Nb-doped TiO2 sintered in air. With the incorporation of 0.5 mol% of Nb2O5, the thermal diffusivity is lower than that of pure TiO2 and shows a steady reduction with temperature. This trend is similar to that of pure TiO2. This could be attributed to Nb impurities acting as the phonon scatterer. In view of the fact that the addition of 0.5 mol% of Nb2O5, will result in the material being semi-conducting [4,5] with electronics transition, it did not seem to contribute to heat conduction above 2008C. However, when 0.7 mol% of Nb2O5 was added, the thermal diffusivity is signi®cantly higher than that with 0.5 mol% of Nb2O5. Below 1508C, the decay of thermal diffusivity versus temperature graph suggests that the dominant contribution to the thermal diffusivity is due to phonon transition. Above 1508C, the thermal diffusivity increases with temperature. This is inconsistent with the phonon scattering theory and hence it is reasonable to conclude that there is another mechanism of thermal diffusivity beside the phonon transition. It is reasonable to conclude that the electronics transition should be taken into account here.
Fig. 3. Thermal diffusivity of Nb-doped and pure TiO2 sintered in air.
476
F. Xiangyi et al. / Journal of Materials Processing Technology 113 (2001) 474±476
effect of electronic transition has a more pronounced effect than that of phonon scattering. 5. Conclusions
Fig. 4. Thermal diffusivity of Ta-doped and pure TiO2.
Fig. 5. Thermal diffusivity of W-doped TiO2.
Fig. 4 shows the thermal diffusivity of Ta-doped TiO2 versus temperature. Compared with Nb-doped samples, Ta doping had not resulted in any reduction of thermal diffusivity. This is contrary to the phonon scattering theory because Eqs. (2) and (3) showed that doping with elements of differing atomic radii would result in mass and strain mis®ts. The resulting mass and strain mis®ts will in theory increase the scattering cross-section, hence reducing the thermal conductivity. Thus, it is suspected that the addition of the Ta impurities that caused the samples to be semiconducting has also resulted in increasing the thermal diffusivity of the material. The thermal diffusivity of W-doped titanium dioxide is shown in Fig. 5. The thermal diffusivities of the doped samples are consistently higher than those of the pure samples for all temperatures and compositions. A peak near 2008C instead of decaying with temperature shows that the
The thermal diffusivity of processed titanium dioxide by reduction and doping with Sn, Nb, W, Ta has been measured. The reduced and Sn-doped TiO2 exhibit a monotonic decay of thermal diffusivity and are consistent with the feature of phonon scattering by vacancy and doped impurities. The thermal diffusivity of Nb-doped TiO2 shows different characteristics with different amount of additives. When the doping amount of Nb is 0.7 mol%, the thermal diffusivity above 1508C tends to increase. This behavior could not be explained only by the phonon scatter theory. A more probable explanation is that the addition of 0.7 mol% of Nb has introduced impurity energy levels in the energy band structure, thus rendering it semi-conducting. Hence an associated increase in thermal conductivity is observed. All the Tadoped samples show monotonic decay of thermal diffusivity but the diffusivity of these samples is still higher than what of pure TiO2. This implies that the doped Ta impurities are not strong phonon scatterers. W doping resulted in a peak in the thermal diffusivity. Acknowledgements This work is supported by the Tan Chin Tuan Fellowship from Nanyang Technological University, Singapore. The assistance of Mr. Huang Haitao, Mrs. Zahara Ahmad and Mrs. Sory is gratefully acknowledged. References [1] C. Kittel, Introduction to Solid-state Physics, 3rd Edition, Wiley, New York, 1967. [2] B. Abeles, Lattice thermal conductivity of disordered semiconductors at high temperatures, Phys. Rev. 131 (5) (1963) 1906±1911. [3] G.A. Slack, Thermal conductivity of MgO, Al2O3, MgAl2O4 and Fe3O4 crystals from 3 to 300 K, Phys. Rev. 126 (2) (1962) 427±441. [4] F. Xiangyi, et al., Semiconducting TiO2 ceramics, J. Mater. Sci. 7 (3) (1993) 245±247 (in Chinese). [5] F. Xiangyi, et al., Research on TiO2 thick ®lm for oxygen sensor, J. Yun Nan Univ. 19 (2) (1997) 135±138 (in Chinese).