- Email: [email protected]
Influence of ball milling parameters on the particle size of barium titanate nanocrystalline powders
ARTICLE IN PRESS Physica B 405 (2010) 430–434
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Influence of ball milling parameters on the particle size of barium titanate nanocrystalline powders A.K. Nath, Chongtham Jiten, K. Chandramani Singh Department of Physics, Sri Venkateswara College, University of Delhi, New Delhi 110021, India
a r t i c l e in f o
a b s t r a c t
Article history: Received 25 July 2009 Accepted 28 August 2009
Barium titanate (BaTiO3 or BT) powder was synthesized from BaCO3–TiO2 reaction at high temperature. This powder was then used to produce BT nanocrystalline powders using high-energy ball milling under different milling conditions. All the milled powders were examined by XRD and TEM. The particle sizes calculated by the Sherrer formula from the XRD patterns agree with the results of TEM images. The particle size was investigated by varying (i) the speed of the mill from 200 to 400 rpm with regular interval of 50 rpm, fixing the milling time at 30 h, and (ii) the milling time from 15 to 40 h, at a fixed speed of 300 rpm. The increase in milling speed results in a gradual reduction in particle size till it finally reaches a saturation value of about 18 nm. However, with increasing milling time, the particle size first decreases, attains a minimum value of about 16 nm and then increases. The involved mechanisms of the observed results are discussed in the present paper. & 2009 Elsevier B.V. All rights reserved.
PACS: 61.46.Hk 75.50.Tt 77.84.Je 78.67.Br 81.05.Je 81.07.Wx Keywords: Barium titanate High-energy milling Milling energy Milling time
1. Introduction Research on lead free piezoelectric ceramics [1,2] has been gaining importance due to the highly toxic nature of lead based piezoelectric ceramics which are otherwise far more superior in piezoelectric properties. BT is one of the most studied lead free materials due to its potential application as multilayer ceramic capacitors, PTC thermistors, piezoelectric transducers, actuators, high-e dielectrics, dynamic RAM and a great variety of electrooptical devices. The characteristics of such electronic ceramic are markedly influenced by the particle size and morphology of the material [3]. A few workers have reported great improvement on the physical, electrical and piezoelectric properties of lead free BT ceramics synthesized from the nanoceramic powders [4–6]. Dielectric constant is also reported to be strongly dependent on the particle size [7–9]. In ferroelectrics such as BT, it is reported that ferroelectricity decreases with decreasing particle size and disappears below certain critical size [10–13]. It is believed that below the critical size the lattice changes from tetragonal to cubic and ferroelectricity is lost. For BT the possible average critical
Corresponding author. Tel.: + 9111 27457625, +91 9868202566; fax: + 9111 24118535. E-mail address: [email protected] (K.C. Singh).
0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.08.299
particle size for ferroelectric behavior in dense BT nanocrystalline ceramics is below 50 nm [14,15]. From these standpoints, production of nanoceramic powders having desired particle size has been gaining importance in recent time. There are other routes for the synthesis of nanoceramic powders such as chemical coprecipitations [16,17], sol–gel technique [18,19], hydrothermal synthesis [20,21]. However, the high-energy ball milling technique is regarded as a simple and cost effective method for large scale production of nanoceramic powders [4,22,23]. Planetary ball mills are widely used as a high-energy ball mill for producing nanometer scale powders of ferroelectric materials. In a planetary ball mill, the grinding jar, mounted on a rotating support frame (called the sun wheel), also rotate around its own axis. The centrifugal forces produced by these two superimposed rotations act on the grinding balls and material inside the jar. As the jar and the supporting frame rotate in opposite directions, the centrifugal forces act alternately in the same and opposite directions. A combination of impact and frictional forces results between the balls and jar, which acts on the material inside the jar. The interplay between these forces is responsible for size reduction of particles and at the same time the microstrains produced in them. The present work deals with the production of BT nanoceramic powders with particle sizes in the range of about 16–80 nm by high-energy ball milling under different milling conditions.
ARTICLE IN PRESS A.K. Nath et al. / Physica B 405 (2010) 430–434
2. Experimental The starting ingredients were AR grade with 99.9% purity powders of BaCO3 and TiO2. The powders were weighed in proportion to the stoichiometric ratio to yield BaTiO3 and then homogeneously mixed in isopropyl alcohol medium using ball milling in plastic bottle with zirconia balls. The mixture was dried and then calcined at 1050 1C for 4 h. The calcined powder was then high-energy milled in the isopropyl alcohol medium using a Retsch PM 100 planetary ball mill in which the sun wheel and grinding jar rotate in opposite directions with speed ratio 1: 2. Agate vial and balls were used. The milling was performed (i) at the speeds of 200, 250, 300, 350 and 400 rpm of the sun wheel, each for 30 h, and (ii) for different durations of 15, 20, 25, 30, 35 and 40 h, fixing the speed at 300 rpm. During each high-energy milling, a mass ratio of 1:5 for powder and balls was always maintained. The planetary ball mill was set to a rotational mode that changes the rotational direction of the vial and the sun wheel every 6 min after a rest interval of 2 min. X-ray Diffractometer PW 3020 with monochromatic CuKa radiation (l = 0.5405 nm) was used over a 2y angle from 201 to 801 to characterize the crystalline phase of the powders milled under different conditions and also to determine the crystallite sizes from the FWHM of the XRD peaks by using the Debye Scherrer formula. The particle sizes of the milled powders were also examined by using TEM (Morgagni 268).
3. Results and discussions It was observed from XRD analysis that all the milled powders crystallize into single phase perovskite structure. Fig. 1 shows a typical XRD pattern for the BT powder which was high-energy milled at the speed of 300 rpm for 30 h. The average particle size ‘‘t’’ is calculated using the Debye Scherrer method from the broadening of the diffraction line using the expression t¼
0:9l b cos y
ð1Þ
where l is the wavelength of the CuKa radiation, b is the FWHM of the diffraction peak and y is the Bragg diffraction angle. The average particle size of all the powders obtained ranges from 20 to 90 nm (calculations were done taking care of the broadening due to the instrument and microstrains). The particle size and morphology of the powders milled at different speeds were examined by TEM. TEM images of the powders produced by milling at the speed of 200, 250, 300, 350 and 400 rpm, each for 30 h are shown in Fig. 2. The corresponding
Fig. 1. X-ray diffraction pattern of a typical BaTiO3 powder milled at 300 rpm for 30 h.
431
average particle sizes evaluated for these BT powders are plotted as a function of the milling speed in Fig. 3. Fig. 3 shows that there is a gradual decrease in the particle size from 80 to 16 nm as the milling speed increases from 200 to 400 rpm. The average particle sizes were also determined from TEM micrographs of the BT powders milled for different durations of 15, 20, 25, 30, 35 and 40 h, each at the speed of 300 rpm. Fig. 4 shows the TEM images of the powders produced under these milling conditions. The variation of the corresponding average particle sizes as a function of the milling time is shown in Fig. 5. As seen in this figure, the particle size first gradually decreases, reaches a minimum and then increases with increase in the milling time. The energy supplied by the planetary ball mill during highenergy milling of a powder is used in the rupture of interatomic bonds in the crystal and the formation of additional surface as a result of the cleavage of crystalline grains [24]. While, because of many different process parameters and conditions, a complete modeling of the milling process would be an aim very difficult to achieve, there have been attempts made in this direction by taking into considerations the kinematics and thermodynamics involved. According to an analytical model proposed by Gusev et al. [25], the dependence of post-milling particle size D of the powders on the milling energy Emill is expressed as D¼
M½A þ BlnðDin =2bÞemax f1 expðctÞg Emill þ M½A þ BlnðDin =2bÞemax f1 expðctÞg=Din
ð2Þ
where M is the mass of the initial powder, Din their initial size, A and B are some constants characteristic of the material, b is the magnitude of Burgers vector associated with a disordered network of edge dislocations in the grains, e = emax[1 exp(ct)] with c o0 is an empirical function describing the dependence of the microstrains e on the milling time t. The energy Emill consumed in milling of the powder is proportional to the cube of the angular rotation speed, o3, and the milling time t, that is Emill ¼ ko3 t
ð3Þ
where k is a constant parameter of the milling system. Using Eq. (3), the relation (2) can be written as D¼
M½A þBlnðDin =2bÞemax f1 expðctÞg ko3 t þM½A þBlnðDin =2bÞemax f1 expðctÞg=Din
ð4Þ
Eq. (4) describes how an increase in the angular rotation speed
o of the ball mill for a fixed milling time t leads to a gradual decrease in the particle size D of the milled powder to a saturation value. This prediction is strongly supported by the observed decrease in the particle size with increasing rpm, as shown in Fig. 3. With increasing rpm the milling energy increases which favors the cleavage of particles producing new finer particles. The saturation in the particle size can be understood in terms of the decreasing impact pressure on the particle. As the particle size of the powder decreases, the number of particles in the zone of the impact point contact with a grinding ball increases leading to the decrease in pressure P imparted to a particle and the gradual cessation of the grinding action. This explains the nature of the experimental plot in Fig. 3 which also shows that the particle size saturates at about 18 nm corresponding to an rpm of 400. According to Eq. (4), for a fixed o, an increase in the milling time should lead to a gradual decrease in the particle size D of the milled powder to a saturation value. Such a decreasing trend of crystal size evolution with the milling time t has also been predicted to be represented by an exponential function of the type [26,27]: D ¼ Df þ ðDin Df Þeðc1 tÞ
ð5Þ
ARTICLE IN PRESS 432
A.K. Nath et al. / Physica B 405 (2010) 430–434
Fig. 2. TEM micrograph of BaTiO3 nanoparticles produced by milling for 30 h at the speed of (a) 200, (b) 250, (c) 300, (d) 350 and (e) 400 rpm.
Fig. 3. Variation of average particle size as a function of rpm.
where D should be considered representative of the crystal size, being Din the initial, Df the steady-state crystal size, and c1 an empirical constant depending on the process parameter. The observed decrease (Fig. 4) in average particle size from 48 nm for powder milled for 15 h to 16 nm for milling time of 25 h agrees with these predictions. Existing theories, however, could not explain the observed increase in particle size from a minimum of 16 nm at 25 h to 38 nm at 40 h of milling. The increase in particle size with milling time could be a complex process involving surface energy and microstrains of the particles. As the particle size goes down to nanometer range the surface to volume ratio of the particle and hence their specific surface energy increases significantly. On the other hand, the microstrains produced in the particles increases as the milling time of the powder increases. Both these processes lead to enhance instability in the powder particles. A critical stage of instability is reached in the system with prolonged grinding when the particles start coalescing to form bigger particles by way of releasing the excess energy. Such an increase of average particle size with increasing ball milling time has also been observed in lead zirconate titanate (PZT) aqueous suspension [28].
ARTICLE IN PRESS A.K. Nath et al. / Physica B 405 (2010) 430–434
433
Fig. 4. TEM micrographs of BaTiO3 nanoparticles produced by milling at the speed of 300 rpm for (a) 15, (b) 20, (c) 25, (d) 30, (e) 35 and (f) 40 h.
4. Conclusion Lead free BT nanocrystalline powders with average particle size as small as 16 nm have been produced by high-energy ball milling. With increasing speed of the ball mill from 200 to 400 rpm at a fixed milling time of 30 h, the particle size of the milled powders decreases gradually till it reaches a saturation value. This observed result agrees with a mathematical model that describes the dependence of post-milling particle size on the rpm of a mill. An increase in milling time from 15 to 25 h at a fixed speed of 300 rpm yields powders with particle size decreasing to a certain minimum and then showing an increase on further increasing the milling time. The increasing trend of particle size with increasing milling time suggests a mechanism in the system that attempts to reverse the ever increasing microstrains and specific surface energy of the grains.
Acknowledgments Fig. 5. Variation of average particle size as a function of milling time.
The financial support from University Grants Commission of India under the Major Research Project Scheme is gratefully
ARTICLE IN PRESS 434
A.K. Nath et al. / Physica B 405 (2010) 430–434
acknowledged. We also acknowledge the Research Section of AIIMS for providing the TEM facility. References [1] Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya, M. Nakamura, Nature 432 (2004) 84. [2] M.D. Maeder, D. Damjanovic, N. Setter, J. Electroceram. 13 (2004) 385. [3] V. Prasad, L. Kumar, Ferroelectrics 102 (1990) 141. [4] L.B. Kong, T.S. Zhang, J. Ma, F. Boey, Progr. Mater. Sci. 53 (2008) 207. [5] T. Karaki, K. Yan, T. Miyamoto, M. Adachi, Japan. J. Appl. Phys. 46 (2007) L97. [6] H. Takahasi, Y. Numamoto, J. Taaani, K. Maatsuta, J. Qiu, S. Tsurekawa, Japan. J. Appl. Phys. 45 (2006) L30. [7] A. Bell, A. Moulson, Ferroelectrics 54 (1984) 147. [8] G. Arlt, D. Hennings, G. Dewith, J. Appl. Phys. 58 (1985) 1619. [9] K. Wu, W. Schltze, J. Amer. Ceram. Soc. 75 (1992) 3390. [10] K. Ishikawa, K. Yoshikawa, N. Okada, Phys. Rev. B 37 (1988) 5852. [11] M.H. Frey, D.A. Payne, Phys. Rev. B 54 (1996) 3158. [12] S. Wada, T. Suzuki, T. Noma, J. Ceram. Soc. Japan 104 (1996) 383. [13] D. McCauley, R.E. Newnham, C.A. Randall, J. Amer. Ceram. Soc. 81 (1998) 979.
[14] L. Mitoseriu, C. Harnagea, P. Nanni, A. Testino, M.T. Buscaglia, V. Buscaglia, M. Viviani, Z. Zhao, M. Nygren, Appl. Phys. Lett. 84 (13) (2004) 2418. [15] Z. Zhao, V. Buscaglia, M. Viviani, M.T. Buscaglia, L. Mitoseriu, A. Testino, M. Nygren, M. Johnsson, P. Nanni, Phys. Rev. B 70 (2004) 024107. [16] A. Testino, T. Buscaglia, M. Viviani, M. Buscaglia, P. Nani, J. Amer. Ceram. Soc. 87 (2004) 79. [17] M. Buscaglia, Z. Zhao, V. Buscaglia, M. Viviani, M.T. Buscaglia, L. Mitoseriu, A. Testino, Nanotechnology 15 (2004) 1113. [18] D. Kang, M. Han, S. Lee, S. Song, J. European Ceram. Soc. 23 (2003) 515. [19] J. Cho, M. Kubawara, J. European Ceram. Soc. 24 (2004) 2959. [20] H. Xu, L. Gao, J. Guo, J. European Ceram. Soc. 22 (2002) 1163. [21] H. Xu, L. Gao, Mater. Lett. 58 (2004) 1582. [22] T. Venugopal, K.P. Rao, B.S. Murty, J. Nanosci. Nanotechnol. 7 (2007) 2376. [23] Y. Wang, Y. Li, C. Rong, P. Liu, J. Nanotechnol. 18 (2007) 465701. [24] P.Y. Butyagin, Chem. Rev. 23 (1998) 91. [25] A.I. Gusev, A.S. Kurlov, Nanotechnology 19 (2008) 1. [26] F. Delogu, M. Monagheddu, G. Mulas, L. Schiffini, G. Cocco, J. Non-Crys. Solids 232-234 (1998) 383. [27] F. Delogu, G. Cocco, Mater. Sci. Eng. A 343 (2003) 314. [28] N. Traiphol, J. Ceram. Processing Res. 8 (2007) 137.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Influence of ball milling parameters on the particle size of barium titanate nanocrystalline powders A.K. Nath, Chongtham Jiten, K. Chandramani Singh Department of Physics, Sri Venkateswara College, University of Delhi, New Delhi 110021, India
a r t i c l e in f o
a b s t r a c t
Article history: Received 25 July 2009 Accepted 28 August 2009
Barium titanate (BaTiO3 or BT) powder was synthesized from BaCO3–TiO2 reaction at high temperature. This powder was then used to produce BT nanocrystalline powders using high-energy ball milling under different milling conditions. All the milled powders were examined by XRD and TEM. The particle sizes calculated by the Sherrer formula from the XRD patterns agree with the results of TEM images. The particle size was investigated by varying (i) the speed of the mill from 200 to 400 rpm with regular interval of 50 rpm, fixing the milling time at 30 h, and (ii) the milling time from 15 to 40 h, at a fixed speed of 300 rpm. The increase in milling speed results in a gradual reduction in particle size till it finally reaches a saturation value of about 18 nm. However, with increasing milling time, the particle size first decreases, attains a minimum value of about 16 nm and then increases. The involved mechanisms of the observed results are discussed in the present paper. & 2009 Elsevier B.V. All rights reserved.
PACS: 61.46.Hk 75.50.Tt 77.84.Je 78.67.Br 81.05.Je 81.07.Wx Keywords: Barium titanate High-energy milling Milling energy Milling time
1. Introduction Research on lead free piezoelectric ceramics [1,2] has been gaining importance due to the highly toxic nature of lead based piezoelectric ceramics which are otherwise far more superior in piezoelectric properties. BT is one of the most studied lead free materials due to its potential application as multilayer ceramic capacitors, PTC thermistors, piezoelectric transducers, actuators, high-e dielectrics, dynamic RAM and a great variety of electrooptical devices. The characteristics of such electronic ceramic are markedly influenced by the particle size and morphology of the material [3]. A few workers have reported great improvement on the physical, electrical and piezoelectric properties of lead free BT ceramics synthesized from the nanoceramic powders [4–6]. Dielectric constant is also reported to be strongly dependent on the particle size [7–9]. In ferroelectrics such as BT, it is reported that ferroelectricity decreases with decreasing particle size and disappears below certain critical size [10–13]. It is believed that below the critical size the lattice changes from tetragonal to cubic and ferroelectricity is lost. For BT the possible average critical
Corresponding author. Tel.: + 9111 27457625, +91 9868202566; fax: + 9111 24118535. E-mail address: [email protected] (K.C. Singh).
0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.08.299
particle size for ferroelectric behavior in dense BT nanocrystalline ceramics is below 50 nm [14,15]. From these standpoints, production of nanoceramic powders having desired particle size has been gaining importance in recent time. There are other routes for the synthesis of nanoceramic powders such as chemical coprecipitations [16,17], sol–gel technique [18,19], hydrothermal synthesis [20,21]. However, the high-energy ball milling technique is regarded as a simple and cost effective method for large scale production of nanoceramic powders [4,22,23]. Planetary ball mills are widely used as a high-energy ball mill for producing nanometer scale powders of ferroelectric materials. In a planetary ball mill, the grinding jar, mounted on a rotating support frame (called the sun wheel), also rotate around its own axis. The centrifugal forces produced by these two superimposed rotations act on the grinding balls and material inside the jar. As the jar and the supporting frame rotate in opposite directions, the centrifugal forces act alternately in the same and opposite directions. A combination of impact and frictional forces results between the balls and jar, which acts on the material inside the jar. The interplay between these forces is responsible for size reduction of particles and at the same time the microstrains produced in them. The present work deals with the production of BT nanoceramic powders with particle sizes in the range of about 16–80 nm by high-energy ball milling under different milling conditions.
ARTICLE IN PRESS A.K. Nath et al. / Physica B 405 (2010) 430–434
2. Experimental The starting ingredients were AR grade with 99.9% purity powders of BaCO3 and TiO2. The powders were weighed in proportion to the stoichiometric ratio to yield BaTiO3 and then homogeneously mixed in isopropyl alcohol medium using ball milling in plastic bottle with zirconia balls. The mixture was dried and then calcined at 1050 1C for 4 h. The calcined powder was then high-energy milled in the isopropyl alcohol medium using a Retsch PM 100 planetary ball mill in which the sun wheel and grinding jar rotate in opposite directions with speed ratio 1: 2. Agate vial and balls were used. The milling was performed (i) at the speeds of 200, 250, 300, 350 and 400 rpm of the sun wheel, each for 30 h, and (ii) for different durations of 15, 20, 25, 30, 35 and 40 h, fixing the speed at 300 rpm. During each high-energy milling, a mass ratio of 1:5 for powder and balls was always maintained. The planetary ball mill was set to a rotational mode that changes the rotational direction of the vial and the sun wheel every 6 min after a rest interval of 2 min. X-ray Diffractometer PW 3020 with monochromatic CuKa radiation (l = 0.5405 nm) was used over a 2y angle from 201 to 801 to characterize the crystalline phase of the powders milled under different conditions and also to determine the crystallite sizes from the FWHM of the XRD peaks by using the Debye Scherrer formula. The particle sizes of the milled powders were also examined by using TEM (Morgagni 268).
3. Results and discussions It was observed from XRD analysis that all the milled powders crystallize into single phase perovskite structure. Fig. 1 shows a typical XRD pattern for the BT powder which was high-energy milled at the speed of 300 rpm for 30 h. The average particle size ‘‘t’’ is calculated using the Debye Scherrer method from the broadening of the diffraction line using the expression t¼
0:9l b cos y
ð1Þ
where l is the wavelength of the CuKa radiation, b is the FWHM of the diffraction peak and y is the Bragg diffraction angle. The average particle size of all the powders obtained ranges from 20 to 90 nm (calculations were done taking care of the broadening due to the instrument and microstrains). The particle size and morphology of the powders milled at different speeds were examined by TEM. TEM images of the powders produced by milling at the speed of 200, 250, 300, 350 and 400 rpm, each for 30 h are shown in Fig. 2. The corresponding
Fig. 1. X-ray diffraction pattern of a typical BaTiO3 powder milled at 300 rpm for 30 h.
431
average particle sizes evaluated for these BT powders are plotted as a function of the milling speed in Fig. 3. Fig. 3 shows that there is a gradual decrease in the particle size from 80 to 16 nm as the milling speed increases from 200 to 400 rpm. The average particle sizes were also determined from TEM micrographs of the BT powders milled for different durations of 15, 20, 25, 30, 35 and 40 h, each at the speed of 300 rpm. Fig. 4 shows the TEM images of the powders produced under these milling conditions. The variation of the corresponding average particle sizes as a function of the milling time is shown in Fig. 5. As seen in this figure, the particle size first gradually decreases, reaches a minimum and then increases with increase in the milling time. The energy supplied by the planetary ball mill during highenergy milling of a powder is used in the rupture of interatomic bonds in the crystal and the formation of additional surface as a result of the cleavage of crystalline grains [24]. While, because of many different process parameters and conditions, a complete modeling of the milling process would be an aim very difficult to achieve, there have been attempts made in this direction by taking into considerations the kinematics and thermodynamics involved. According to an analytical model proposed by Gusev et al. [25], the dependence of post-milling particle size D of the powders on the milling energy Emill is expressed as D¼
M½A þ BlnðDin =2bÞemax f1 expðctÞg Emill þ M½A þ BlnðDin =2bÞemax f1 expðctÞg=Din
ð2Þ
where M is the mass of the initial powder, Din their initial size, A and B are some constants characteristic of the material, b is the magnitude of Burgers vector associated with a disordered network of edge dislocations in the grains, e = emax[1 exp(ct)] with c o0 is an empirical function describing the dependence of the microstrains e on the milling time t. The energy Emill consumed in milling of the powder is proportional to the cube of the angular rotation speed, o3, and the milling time t, that is Emill ¼ ko3 t
ð3Þ
where k is a constant parameter of the milling system. Using Eq. (3), the relation (2) can be written as D¼
M½A þBlnðDin =2bÞemax f1 expðctÞg ko3 t þM½A þBlnðDin =2bÞemax f1 expðctÞg=Din
ð4Þ
Eq. (4) describes how an increase in the angular rotation speed
o of the ball mill for a fixed milling time t leads to a gradual decrease in the particle size D of the milled powder to a saturation value. This prediction is strongly supported by the observed decrease in the particle size with increasing rpm, as shown in Fig. 3. With increasing rpm the milling energy increases which favors the cleavage of particles producing new finer particles. The saturation in the particle size can be understood in terms of the decreasing impact pressure on the particle. As the particle size of the powder decreases, the number of particles in the zone of the impact point contact with a grinding ball increases leading to the decrease in pressure P imparted to a particle and the gradual cessation of the grinding action. This explains the nature of the experimental plot in Fig. 3 which also shows that the particle size saturates at about 18 nm corresponding to an rpm of 400. According to Eq. (4), for a fixed o, an increase in the milling time should lead to a gradual decrease in the particle size D of the milled powder to a saturation value. Such a decreasing trend of crystal size evolution with the milling time t has also been predicted to be represented by an exponential function of the type [26,27]: D ¼ Df þ ðDin Df Þeðc1 tÞ
ð5Þ
ARTICLE IN PRESS 432
A.K. Nath et al. / Physica B 405 (2010) 430–434
Fig. 2. TEM micrograph of BaTiO3 nanoparticles produced by milling for 30 h at the speed of (a) 200, (b) 250, (c) 300, (d) 350 and (e) 400 rpm.
Fig. 3. Variation of average particle size as a function of rpm.
where D should be considered representative of the crystal size, being Din the initial, Df the steady-state crystal size, and c1 an empirical constant depending on the process parameter. The observed decrease (Fig. 4) in average particle size from 48 nm for powder milled for 15 h to 16 nm for milling time of 25 h agrees with these predictions. Existing theories, however, could not explain the observed increase in particle size from a minimum of 16 nm at 25 h to 38 nm at 40 h of milling. The increase in particle size with milling time could be a complex process involving surface energy and microstrains of the particles. As the particle size goes down to nanometer range the surface to volume ratio of the particle and hence their specific surface energy increases significantly. On the other hand, the microstrains produced in the particles increases as the milling time of the powder increases. Both these processes lead to enhance instability in the powder particles. A critical stage of instability is reached in the system with prolonged grinding when the particles start coalescing to form bigger particles by way of releasing the excess energy. Such an increase of average particle size with increasing ball milling time has also been observed in lead zirconate titanate (PZT) aqueous suspension [28].
ARTICLE IN PRESS A.K. Nath et al. / Physica B 405 (2010) 430–434
433
Fig. 4. TEM micrographs of BaTiO3 nanoparticles produced by milling at the speed of 300 rpm for (a) 15, (b) 20, (c) 25, (d) 30, (e) 35 and (f) 40 h.
4. Conclusion Lead free BT nanocrystalline powders with average particle size as small as 16 nm have been produced by high-energy ball milling. With increasing speed of the ball mill from 200 to 400 rpm at a fixed milling time of 30 h, the particle size of the milled powders decreases gradually till it reaches a saturation value. This observed result agrees with a mathematical model that describes the dependence of post-milling particle size on the rpm of a mill. An increase in milling time from 15 to 25 h at a fixed speed of 300 rpm yields powders with particle size decreasing to a certain minimum and then showing an increase on further increasing the milling time. The increasing trend of particle size with increasing milling time suggests a mechanism in the system that attempts to reverse the ever increasing microstrains and specific surface energy of the grains.
Acknowledgments Fig. 5. Variation of average particle size as a function of milling time.
The financial support from University Grants Commission of India under the Major Research Project Scheme is gratefully
ARTICLE IN PRESS 434
A.K. Nath et al. / Physica B 405 (2010) 430–434
acknowledged. We also acknowledge the Research Section of AIIMS for providing the TEM facility. References [1] Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya, M. Nakamura, Nature 432 (2004) 84. [2] M.D. Maeder, D. Damjanovic, N. Setter, J. Electroceram. 13 (2004) 385. [3] V. Prasad, L. Kumar, Ferroelectrics 102 (1990) 141. [4] L.B. Kong, T.S. Zhang, J. Ma, F. Boey, Progr. Mater. Sci. 53 (2008) 207. [5] T. Karaki, K. Yan, T. Miyamoto, M. Adachi, Japan. J. Appl. Phys. 46 (2007) L97. [6] H. Takahasi, Y. Numamoto, J. Taaani, K. Maatsuta, J. Qiu, S. Tsurekawa, Japan. J. Appl. Phys. 45 (2006) L30. [7] A. Bell, A. Moulson, Ferroelectrics 54 (1984) 147. [8] G. Arlt, D. Hennings, G. Dewith, J. Appl. Phys. 58 (1985) 1619. [9] K. Wu, W. Schltze, J. Amer. Ceram. Soc. 75 (1992) 3390. [10] K. Ishikawa, K. Yoshikawa, N. Okada, Phys. Rev. B 37 (1988) 5852. [11] M.H. Frey, D.A. Payne, Phys. Rev. B 54 (1996) 3158. [12] S. Wada, T. Suzuki, T. Noma, J. Ceram. Soc. Japan 104 (1996) 383. [13] D. McCauley, R.E. Newnham, C.A. Randall, J. Amer. Ceram. Soc. 81 (1998) 979.
[14] L. Mitoseriu, C. Harnagea, P. Nanni, A. Testino, M.T. Buscaglia, V. Buscaglia, M. Viviani, Z. Zhao, M. Nygren, Appl. Phys. Lett. 84 (13) (2004) 2418. [15] Z. Zhao, V. Buscaglia, M. Viviani, M.T. Buscaglia, L. Mitoseriu, A. Testino, M. Nygren, M. Johnsson, P. Nanni, Phys. Rev. B 70 (2004) 024107. [16] A. Testino, T. Buscaglia, M. Viviani, M. Buscaglia, P. Nani, J. Amer. Ceram. Soc. 87 (2004) 79. [17] M. Buscaglia, Z. Zhao, V. Buscaglia, M. Viviani, M.T. Buscaglia, L. Mitoseriu, A. Testino, Nanotechnology 15 (2004) 1113. [18] D. Kang, M. Han, S. Lee, S. Song, J. European Ceram. Soc. 23 (2003) 515. [19] J. Cho, M. Kubawara, J. European Ceram. Soc. 24 (2004) 2959. [20] H. Xu, L. Gao, J. Guo, J. European Ceram. Soc. 22 (2002) 1163. [21] H. Xu, L. Gao, Mater. Lett. 58 (2004) 1582. [22] T. Venugopal, K.P. Rao, B.S. Murty, J. Nanosci. Nanotechnol. 7 (2007) 2376. [23] Y. Wang, Y. Li, C. Rong, P. Liu, J. Nanotechnol. 18 (2007) 465701. [24] P.Y. Butyagin, Chem. Rev. 23 (1998) 91. [25] A.I. Gusev, A.S. Kurlov, Nanotechnology 19 (2008) 1. [26] F. Delogu, M. Monagheddu, G. Mulas, L. Schiffini, G. Cocco, J. Non-Crys. Solids 232-234 (1998) 383. [27] F. Delogu, G. Cocco, Mater. Sci. Eng. A 343 (2003) 314. [28] N. Traiphol, J. Ceram. Processing Res. 8 (2007) 137.