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In situ TEM sintering of nano-sized ZrO2 particles
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Materials Scienceand EngineeringA204 (t995) 48 53
In situ TEM sintering of nano-sized ZrO2 particles J. Rankin*, B.W. Sheldon Division of Engineering, Bro~,n University, Providence, RI 02912, USA
Abstract The sintering behavior of faceted, nano-sized single-crystal particles of Z r O 2 has been investigated using in situ transmission electron microscope heating techniques. These direct observations have provided new information on the morphological and structural evolution of particles, necks and pores during the sintering process. The results indicate that ZrO2 particle-pairs, which are not attached to other particles and not highly constrained by the TEM grid, reorient themselves with respect to each other during sintering at 890°C. This reorientation can be explained in terms of a minimization of the grain-boundary energy between the two coalescing particles. In addition to changes in particle orientation, these experiments show that the topologies of ZrO 2 particles and their associated necks evolve during heating. During the in situ TEM heating of these particles, the dynamic motion of atom clusters (10-100 atoms) on and off of surfaces is observed, as is the formation and dissolution of ledges and steps on previously smooth facets. The phenomenon of cluster migration is discussed and the ramifications of the results of this study for more highly constrained systems of particles (e.g, ceramic green-bodies) are also considered. Keywords: In situ TEM: Nanoscale; Sintering; Z r O 2
1. Introduction and background The sintering process is of tremendous technological importance due to its widespread use in the manufacture of ceramic materials and in powder metallurgy. Most previous investigations of early stage sintering in ceramic powders have employed ex situ heating in idealized systems consisting of polycrystalline micronsized particles with circular cross-sections [1,2]. Numerous researchers have examined particle, neck, and pore morphology changes in ex situ sintered, micron-sized polycrystalline powders [3]. In recent years, several ex-situ studies of sintering single crystal particles of micron-sized ZrO2 [4] and nano-sized A120 3 [5,6] have been reported. Although these studies represent significant contributions to the field of sintering, their ex situ nature limits measurements of the neck and particle size and morphology to average values over the total time of the heating cycle. In contrast, in situ heating allows morphology and size to be measured continuously throughout the experiment, and provides the most ac-
* Corresponding author.
curate means of monitoring and understanding the evolution of the nano-scale microstructure. With a few notable exceptions [7 9,11,12] ex situ studies have essentially dominated previous experimental studies of the evolution of neck and pore morphologies that occur during heating. Recent studies of the in situ TEM sintering of submicron, single-crystal, faceted MgO particles show that the contact geometry is critical in determining the sintering behavior of two adjacent particles [9]. In fact, it has been shown that particles that are in contact over small areas can actually desinter during the heating process. Ultimately, two individual particles are created, with no neck between them. Theoretical investigations that consider the precise role of the facets on this process have also been undertaken [10]. Fujita [11] has studied the in situ heating behavior of coarse-grained ( ~ 1 ~m), A1203, A1203 + M g O and Z r O 2 + A1203 ceramics using high-voltage electron microscopy. In these studies a circular area approximately 8 /~m in diameter was viewed. In light of the successes and shortcomings of the studies discussed above, the primary objectives of the present in situ TEM heating investigation were: 0921-5093/95/$09.50 © 1995
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J. Rankm. B.W. SheMon / Materials Science and Engineering A204 (1995) 48-53
(1) to observe particle reorientation and neck growth, and (2) to further invesigate the origins and ramifications of the observed surface fluctuations.
2. Experimental procedure Nano-sized powders are ideally suited for TEM studies, because their small size permits high-resolution imaging without significant sample preparation (no thinning of any kind is required). As a consequence, no artifacts associated with the thinning process (e.g. dislocations) are introduced into the samples. By utilizing a novel reactor design, nano-sized, single-crystal particles of ZrO~ (with a mixture of tetragonal and monoclinic phases) were produced by the turbulent combustion of aerosols of organo-metallic precursors [13]. The particles were subsequently suspended in acetone and deposited on a thin amorphous carbon layer on a molybdenum grid. Molybdenum was chosen because it neither melts nor alloys with the tantalum heatingholder at temperatures between room temperature and 1300°C. Using a Gatan single-tilt heating holder in a JEOL 2010 transmission electron microscope, the particles were heated to one of two temperatures (890°C and l l00 °C). As a result of thermal gradients across the TEM grid, it is estimated that the actual sample temperature is within ~ 50°C of the thermocouple temperature. Since all of the samples investigated during this part of the study were mounted on the same type of grid, it is reasonable to expect that the thermal contact was essentially the same in all samples. Furthermore, the carbon substrate exhibited significant fluctuations when the thermocouple reading was (900 _+ 10)°C, indicating reproducible temperatures. These fluctuations subsided after approximately 15 rain, at which point it was possible to obtain good quality T E M images. The data were collected on videotape, which was subsequently analyzed to determine crystallographic relations and growth rates. Some important characteristics of the ZrO~ particles studied here are enumerated below: (1) The particles are 20-200 nm diameter, singlecrystals. (2) There are no internal grain boundaries within the coalescing grains (only at the junction between the two particles). (3) The heating experiments were performed within the vacuum of a transmission electron microscope ( ~ 1 0 v atm). (4) The heating experiments were monitored and continuously recorded using a video recorder. This allowed individual particle pairs to be observed throughout their evolution.
49
3. Results and discussion Preliminary results on the in situ sintering of ZrO2 faceted particles can be divided into two distinct categories: those related to particle reorientation during the sintering of two adjacent particles, and those associated with changes in the atomic arrangement of particle surfaces during heating. Observations of the behavior of pairs of ZrO 2 particles at ~ 890°C reveal particle reorientation during sintering. Although a similar behavior has been observed elsewhere [7,9,12,14] the high-resolution techniques utilized in the present study can provide detailed, dynamic orientational information. At the start of the experiment, as seen in Fig. l(a), the particle marked '1' is oriented such that cross-fringes are visible, and the second particle, marked '2', is not oriented with any particular zone axis parallel to the electron beam (no fringes are visible). In general it can be assumed that as long as a zone axis is within ~ 8 ° of the electron beam, the cross-fringes associated with that particular zone will be resolvable. As heating continues, one of the particles moves (presumably to minimize the energy associated with the boundary between the two particles), and one set of fringes becomes visible in the second particle (see Fig. l(b)). Finally, after approximately 1 h, lattice fringes can be seen in the second (previously unaligned) particle, while the initial crossfringes are still visible in the first particle. One set of fringes is clearly parallel in the two particles indicating a larger degree of alignment than originally existed. It should be noted that the first particle has not moved more than approximately 8 ° (the original cross-fringes are still visible), while the second particle has moved appreciably. It is likely that the first particle was more strongly attached to the carbon film (on which the powders were dispersed), and thus its motion was prevented. For the case of unconstrained particles in contact (as is the case in the previous example), the lowest energy configuration obviously exists when the two particles form an uninterrupted single crystal across their surfaces of contact (i.e. when there is no crystallographic mismatch and therefore no grain boundary). The situation becomes more complicated when the particles are constrained by attachments to other particles. In the case of multiple particles, a reduction of all of the grain boundary energies to form a continuous crystal across contact surfaces is highly unlikely, and the lowest energy state for this configuration would most likely be accomplished through a variety of permutations of orientations of the consituent particles. In addition to orientational information, the images of Figs. l(a)-(c) can be used to determine neck radius as a function of time; similar measurements have been made in the MgO system [9]. On the basis of these
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J. Rankin, B. lie Sheldon / Materials Science and Engineering A204 (1995) 48 53
measurements, the radius of the neck increases about 18% during this experiment. For all particle pairs observed, the neck radius reached a maximum and did not
appear to change in size past that point. This is consistent with the findings of other investigators. In previous studies it has been found that necks between micronsized, spherical, single crystal ZrO 2 particles reach a static size, corresponding to a balance between the energy required to create a new grain boundary area and the energy supplied as the overall surface area of the two-particle system decreases [4]. These findings are obviously applicable here, but must be reinterpreted to account for the rearrangement of the particles in order to minimize the contribution of grain boundary energy to the energy of the entire system. Since no approach of particle centers is measured, surface diffusion and evaporation-condensation are the most probable mechanisms for mass transport, since they do not lead to densification. In general, a maxim u m evaporation rate can be estimated with a Langmuir evaporation flux equation:
(a)
Jevap -
(b)
P (27rMR T) 1'2'
( 1)
where P and M are the equilibrium vapor pressure and molecular weight of the rate-limiting species, respectively, T is the absolute temperature, and R is the gas constant. For ZrO 2 in a vacuum of 10 7 atm at 1000°C the maximum evaporation rate is found to be 0.2 nm h 1 (p was estimated using S O L G A S M I X PV [15]). Experimentally, the size of the particles does not decrease significantly, confirming that evaporation effects are not significant in this system. It should be noted that volume diffusion may play a role in the redistribution of material without a resultant particle center approach, if the particles themselves are constrained through attachment to adjacent particles. Order-of-magnitude estimates which assume that volume diffusion is the only operative transport mechanism indicate that it would take ~ l0 s s to move an atom 100 nm from the center of a particle to the neck region; this is much slower than the timescales that were studied. Since surface diffusion is the dominant transport mechanism, the positive radius of curvature can be related to the time that the neck has been growing through a standard power law dependence (derived by assuming spherical particles and isotropic surface energies): x = [Kt] 1'7.
(2)
The value of the constant K is obtained from a regression of the data, and can be related to several system parameters as given below [16]:
56~R3yD~ds kbT
(c)
K-
(3)
Fig. 1. High-resolution still images taken from real-time videotape monitoring of the neck region between two ZrO 2 particles after: (a) 30 rain, (b) 60 rain, and (c) 90 min at (890 _+30)°C.
where f~ is the molar volume, R is the radius of the sintering particles (assumed to be spherical), 7 is the
J. Rankin, B.W. Sheldon / MateriaL~ Science and Engineerin¢ A204 (1995) 48 53
surface energy (assumed to be isotropic), c5s is the surface layer thickness, k b is Boltzman's constant, and T is the absolute temperature. By substituting appropriate values of 7, E2, R, ~5, ]¢b, and T in the equation above, the surface diffusion coefficient, D~, can be estimated; at 890°C it is found to be between 10 12 and 10-13 cm 2 s t. The second noteworthy phenomenon in the ZrO2 system is the fluctuations on the surfaces of these particles at ~ I I00°C. This phenomenon has been observed in ZrO2 [13] and in small gold particles [17]. Because of the nature of high-resolution T E M imaging, single atoms are not detectable, that is, the electron beam must pass through a minimum thickness of material (approximately 3 to 7 unit cells before imaging is possible). When cross-fringes are visible, the sample is oriented with the zone-axis parallel to the electron beam, in which case the T E M image is formed by the passage of the electron beam through columns of atoms which are parallel to the zone-axis. When part of a T E M image 'disappears' it indicates that less than a critical number of atoms remain in a particular column. Therefore, it is logical to conclude that the observed fluctuations arise from the motion or 'hopping' of clusters of atoms on and off of the surfaces of the particles. An example of this cluster motion can be seen in Figs. 2(a)-(c). Each number in Fig. 2 indicates the location of a different column of atoms. The column marked with a '1' is visible in Fig 2(a), but not visible in Fig 2(b), and is visible again in Fig 2(c). Similarly, the site marked with a '2' appears to be filled in Figs. 2(a) and (b), but is not visible in Fig. 2(c). A '3' marks the site where a column is not visible in Fig. 2(a), whereas this site appears to be filled in Fig. 2(b), and is not visible (along with the atoms in site '2') in Fig. 2(c). The images shown here are taken from a videotape of the in situ heating process, and span a time of approximately 5 s. Measurements from the videotape of the frequency of the motion of clusters on and off of the surface, together with a simplified random-walk calculation, Eq. (4) below, can be used to estimate a diffusion coefficient for this phenomenon. It should be noted that the oscillations observed here reflect the motion of columns of atoms, not the motion of individual atoms normally associated with a random-walk description of surface diffusion [18]: F D = ~ nr -.
51
(a)
~b)
(4)
The quantity F is the j u m p rate of the column of atoms, and is estimated to be ~ 2 s 1. The j u m p distance r is of the order of one lattice spacing ( ~ 0.4 nm), and the number of atoms per column n is probably between 10 and 100. Using these values, the diffusion coefficient is calculated as 2(10) 14 to 2(10) ~3 cm 2 S 1.
(c) Fig, 2. High-resolution still images taken from real-time videotape monitoring of the edge of a Z r O 2 particle. l-he total elapsed time between images (a) and (c) is ~ 5 seconds. The numbers in these images denote the location of columns of atoms which appear and disappear over the course of the experiment.
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J. Rankin, B.W. Sheldon / Materials' Science and Engineering A204 (1995) 48 53
Recently Kusunoki et al. [12] have made in situ observations of nano-sized ZrO2 at l l00°C and have reported the occurrence of surface fluctuations (similar to those observed here). They have suggested that these fluctuations correspond to surface diffusion. However, D~ values obtained from the rate of neck growth (i.e. with Eq. (3)) are considerably larger than values obtained from the observed fluctuations (i.e. with Eq. (4)). It is important to note that the estimates made with Eqs. (3) and (4) are approximate, and are probably only accurate to within one or two orders of magnitude. However, the calculations made with Eq. (3) are based on neck growth rates that were measured at a lower temperature (890°C) than the surface fluctuation measurements (ll00°C), therefore the flux associated with neck growth is almost certainly much larger than the flux associated with surface fluctuations. Even though the observed rate of surface fluctuations is apparently too low to directly account for neck growth, the surface fluctuations are still probably related to surface mobilities. Instead of the traditional picture of individual atoms moving randomly along a relatively static surface, it appears that surface atoms can form clusters that essentially move as a unit. Additional studies are currently underway to elucidate this phenomenon. It should be noted that surface oscillations and reconstruction have been observed at both room temperature and elevated temperatures in other systems such as CdTe and CdS, where they have been attributed to electron beam-solid interactions at room temperature and thermal effects at higher temperatures [19,20]. Related studies [21] suggest that electron beam irradiation is responsible for enhanced atomic mobility and dislocation motion at lower temperatures, whereas at higher temperatures the dislocation velocities are thermally activated and exhibit standard Arrhenius-type behavior. In other studies, the electron beam has been shown to induce a room temperature reduction of irradiated surfaces of transition metal oxides to yield either the metal [22], or a lower oxide [23]. In those studies, the frequency of surface oscillation or phase transformation was found to be strongly dependent on the electron beam current and the time of exposure. For the results reported here the incident beam current was varied with no effect on the nature of the oscillations. Additionally, it should be noted that no oscillations are observed at temperatures less than ~ 1000°C even though, as previously discussed, neck growth via surface occurs at 890°C. These observations confirm that the oscillations are thermally induced.
4. Summary In situ TEM heating studies of Zr02 have provided new insights into the sintering process. Specifically, it
has been shown that: (1) Unconstrained, single-crystal particles of ZrO2 in contact with only one other particle reorient during heating at 890°C. (2) Neck growth during the early stages of sintering occurs at 890°C. However, at longer times, the necks reach a static size. This observation is in good agreement with the results of other researchers [4]. Measurements of the neck radius as a function of time are used to provide an estimate of the surface diffusion coefficient at this temperature. (3) Surface fluctuations are observed when ZrO~ particles are heated to temperatures greater than 1000°C. These fluctuations are associated with the motion of clusters of atoms, and do not appear to be direct evidence of 'traditional' surface diffusion. Additional experiments are essential if the origins and ramifications of cluster migration in this system are to be thoroughly understood.
Acknowledgments We wish to thank L.A. Boatner and A.F. Schwartzman for their valuable discussions and comments, and the National Science Foundation for providing the funding for this research.
References [I] G.C. Kuczynski, d. Trans. A1ME, 185 (1949) 796. [2] W.D. Kingery and M. Berg, d. Appl. Phys., 26(10) (1955) 1205. [3] S. Somiya and Y. Moriyoshi (eds.), Smtering Key Papers, Elsevier Science Publishing Co., Inc., New York, NY, 1990. [4] E.B Slamovich and F. Lange, J. Am. Ceram. Sot., 73(11) (1990) 3368. [5] J.E. Bonevich and L.D. Marks, d. Mater. Res., 7(6)(1992) 1489. [6] S. Ijima, Y. Electron Mierosc., 34 (1985) 249. [7] K.E. Easterling and A.R. Tholen, Met. Sei. J,, 4 (19701 130. [8] 1. Hansson and A. Tholen, Phil. Mag. A., 37(1978) 535. [9] J. Rankin and L.A. Boatner, J. Am. Ceram. Sot., 77(8) (1994) 1987. [10] W.C. Carter, A.R. Roosen and J.W. Cahn, Oral Presentation at the 96th Annual Meeting of the American Ceramic Society, Indianapolis, IN, 24 27 April 1994 (talk no. SV-I 1-94). [11] H. Fujita, J. Electron Microsc. Technol., 12 (1989) 201. [12] M. Kusunoki, K.Yonemitsu, Y. Sasaki and Y. Kubo. J. Am. Ceram. Sot., 76 (1993) 763. [13] A. Kilian, Ph.D. Thesis, Brown University, Division of Engineering, May 1994. [14] G. Petzow and H.E. Exner~ Z. Metall., 67 (1976) 611. [15] T. Besmann, SOLGASM1X-PV, ORNL/TM-5775, Oak Ridge National Laboratory, Oak Ridge, TN, 1977. [16] D. Uskokovic and H.E. Exner, Sci. Sh~tering, 9(3) (1977) 265. [17] O. Bovin, R. Wallenberg and D.J. Smith, Nature, 317 (1985) 47. [18] P~ Shewmon, D(ffi~sion in Solids, J. Williams Book Co., Jenks, OK, 1983, p. 47.
J. Rankin+ B.W. Sheldon / MateriaL~ Science and Engineering A204 (1995) 48 5,7 [19] P. Lu and D.J Smith, Phys. Rev. Lett., 59 (1987) 2177. [20] D.J. Ehrlich and D.J. Smith, Appl. Phys. Lett., 48 (1986) 1751. [21] K. Maeda and S. Takeuchi, Appl. Phys. Lett., 42 (1983) 664.
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[22] A.K. Petford, L.D. Marks and M. O'Keeffe, Sugi Sci., 172 (1986) 496. [23] D.J. Smith, M.R. McCartney and L.A. Bursill, Ultramicroscopy, 23 (1987) 299.
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In situ TEM sintering of nano-sized ZrO2 particles J. Rankin*, B.W. Sheldon Division of Engineering, Bro~,n University, Providence, RI 02912, USA
Abstract The sintering behavior of faceted, nano-sized single-crystal particles of Z r O 2 has been investigated using in situ transmission electron microscope heating techniques. These direct observations have provided new information on the morphological and structural evolution of particles, necks and pores during the sintering process. The results indicate that ZrO2 particle-pairs, which are not attached to other particles and not highly constrained by the TEM grid, reorient themselves with respect to each other during sintering at 890°C. This reorientation can be explained in terms of a minimization of the grain-boundary energy between the two coalescing particles. In addition to changes in particle orientation, these experiments show that the topologies of ZrO 2 particles and their associated necks evolve during heating. During the in situ TEM heating of these particles, the dynamic motion of atom clusters (10-100 atoms) on and off of surfaces is observed, as is the formation and dissolution of ledges and steps on previously smooth facets. The phenomenon of cluster migration is discussed and the ramifications of the results of this study for more highly constrained systems of particles (e.g, ceramic green-bodies) are also considered. Keywords: In situ TEM: Nanoscale; Sintering; Z r O 2
1. Introduction and background The sintering process is of tremendous technological importance due to its widespread use in the manufacture of ceramic materials and in powder metallurgy. Most previous investigations of early stage sintering in ceramic powders have employed ex situ heating in idealized systems consisting of polycrystalline micronsized particles with circular cross-sections [1,2]. Numerous researchers have examined particle, neck, and pore morphology changes in ex situ sintered, micron-sized polycrystalline powders [3]. In recent years, several ex-situ studies of sintering single crystal particles of micron-sized ZrO2 [4] and nano-sized A120 3 [5,6] have been reported. Although these studies represent significant contributions to the field of sintering, their ex situ nature limits measurements of the neck and particle size and morphology to average values over the total time of the heating cycle. In contrast, in situ heating allows morphology and size to be measured continuously throughout the experiment, and provides the most ac-
* Corresponding author.
curate means of monitoring and understanding the evolution of the nano-scale microstructure. With a few notable exceptions [7 9,11,12] ex situ studies have essentially dominated previous experimental studies of the evolution of neck and pore morphologies that occur during heating. Recent studies of the in situ TEM sintering of submicron, single-crystal, faceted MgO particles show that the contact geometry is critical in determining the sintering behavior of two adjacent particles [9]. In fact, it has been shown that particles that are in contact over small areas can actually desinter during the heating process. Ultimately, two individual particles are created, with no neck between them. Theoretical investigations that consider the precise role of the facets on this process have also been undertaken [10]. Fujita [11] has studied the in situ heating behavior of coarse-grained ( ~ 1 ~m), A1203, A1203 + M g O and Z r O 2 + A1203 ceramics using high-voltage electron microscopy. In these studies a circular area approximately 8 /~m in diameter was viewed. In light of the successes and shortcomings of the studies discussed above, the primary objectives of the present in situ TEM heating investigation were: 0921-5093/95/$09.50 © 1995
ElsevierScience S.A. All rights reserved SSDI 0921-5093(95)09936-0
J. Rankm. B.W. SheMon / Materials Science and Engineering A204 (1995) 48-53
(1) to observe particle reorientation and neck growth, and (2) to further invesigate the origins and ramifications of the observed surface fluctuations.
2. Experimental procedure Nano-sized powders are ideally suited for TEM studies, because their small size permits high-resolution imaging without significant sample preparation (no thinning of any kind is required). As a consequence, no artifacts associated with the thinning process (e.g. dislocations) are introduced into the samples. By utilizing a novel reactor design, nano-sized, single-crystal particles of ZrO~ (with a mixture of tetragonal and monoclinic phases) were produced by the turbulent combustion of aerosols of organo-metallic precursors [13]. The particles were subsequently suspended in acetone and deposited on a thin amorphous carbon layer on a molybdenum grid. Molybdenum was chosen because it neither melts nor alloys with the tantalum heatingholder at temperatures between room temperature and 1300°C. Using a Gatan single-tilt heating holder in a JEOL 2010 transmission electron microscope, the particles were heated to one of two temperatures (890°C and l l00 °C). As a result of thermal gradients across the TEM grid, it is estimated that the actual sample temperature is within ~ 50°C of the thermocouple temperature. Since all of the samples investigated during this part of the study were mounted on the same type of grid, it is reasonable to expect that the thermal contact was essentially the same in all samples. Furthermore, the carbon substrate exhibited significant fluctuations when the thermocouple reading was (900 _+ 10)°C, indicating reproducible temperatures. These fluctuations subsided after approximately 15 rain, at which point it was possible to obtain good quality T E M images. The data were collected on videotape, which was subsequently analyzed to determine crystallographic relations and growth rates. Some important characteristics of the ZrO~ particles studied here are enumerated below: (1) The particles are 20-200 nm diameter, singlecrystals. (2) There are no internal grain boundaries within the coalescing grains (only at the junction between the two particles). (3) The heating experiments were performed within the vacuum of a transmission electron microscope ( ~ 1 0 v atm). (4) The heating experiments were monitored and continuously recorded using a video recorder. This allowed individual particle pairs to be observed throughout their evolution.
49
3. Results and discussion Preliminary results on the in situ sintering of ZrO2 faceted particles can be divided into two distinct categories: those related to particle reorientation during the sintering of two adjacent particles, and those associated with changes in the atomic arrangement of particle surfaces during heating. Observations of the behavior of pairs of ZrO 2 particles at ~ 890°C reveal particle reorientation during sintering. Although a similar behavior has been observed elsewhere [7,9,12,14] the high-resolution techniques utilized in the present study can provide detailed, dynamic orientational information. At the start of the experiment, as seen in Fig. l(a), the particle marked '1' is oriented such that cross-fringes are visible, and the second particle, marked '2', is not oriented with any particular zone axis parallel to the electron beam (no fringes are visible). In general it can be assumed that as long as a zone axis is within ~ 8 ° of the electron beam, the cross-fringes associated with that particular zone will be resolvable. As heating continues, one of the particles moves (presumably to minimize the energy associated with the boundary between the two particles), and one set of fringes becomes visible in the second particle (see Fig. l(b)). Finally, after approximately 1 h, lattice fringes can be seen in the second (previously unaligned) particle, while the initial crossfringes are still visible in the first particle. One set of fringes is clearly parallel in the two particles indicating a larger degree of alignment than originally existed. It should be noted that the first particle has not moved more than approximately 8 ° (the original cross-fringes are still visible), while the second particle has moved appreciably. It is likely that the first particle was more strongly attached to the carbon film (on which the powders were dispersed), and thus its motion was prevented. For the case of unconstrained particles in contact (as is the case in the previous example), the lowest energy configuration obviously exists when the two particles form an uninterrupted single crystal across their surfaces of contact (i.e. when there is no crystallographic mismatch and therefore no grain boundary). The situation becomes more complicated when the particles are constrained by attachments to other particles. In the case of multiple particles, a reduction of all of the grain boundary energies to form a continuous crystal across contact surfaces is highly unlikely, and the lowest energy state for this configuration would most likely be accomplished through a variety of permutations of orientations of the consituent particles. In addition to orientational information, the images of Figs. l(a)-(c) can be used to determine neck radius as a function of time; similar measurements have been made in the MgO system [9]. On the basis of these
50
J. Rankin, B. lie Sheldon / Materials Science and Engineering A204 (1995) 48 53
measurements, the radius of the neck increases about 18% during this experiment. For all particle pairs observed, the neck radius reached a maximum and did not
appear to change in size past that point. This is consistent with the findings of other investigators. In previous studies it has been found that necks between micronsized, spherical, single crystal ZrO 2 particles reach a static size, corresponding to a balance between the energy required to create a new grain boundary area and the energy supplied as the overall surface area of the two-particle system decreases [4]. These findings are obviously applicable here, but must be reinterpreted to account for the rearrangement of the particles in order to minimize the contribution of grain boundary energy to the energy of the entire system. Since no approach of particle centers is measured, surface diffusion and evaporation-condensation are the most probable mechanisms for mass transport, since they do not lead to densification. In general, a maxim u m evaporation rate can be estimated with a Langmuir evaporation flux equation:
(a)
Jevap -
(b)
P (27rMR T) 1'2'
( 1)
where P and M are the equilibrium vapor pressure and molecular weight of the rate-limiting species, respectively, T is the absolute temperature, and R is the gas constant. For ZrO 2 in a vacuum of 10 7 atm at 1000°C the maximum evaporation rate is found to be 0.2 nm h 1 (p was estimated using S O L G A S M I X PV [15]). Experimentally, the size of the particles does not decrease significantly, confirming that evaporation effects are not significant in this system. It should be noted that volume diffusion may play a role in the redistribution of material without a resultant particle center approach, if the particles themselves are constrained through attachment to adjacent particles. Order-of-magnitude estimates which assume that volume diffusion is the only operative transport mechanism indicate that it would take ~ l0 s s to move an atom 100 nm from the center of a particle to the neck region; this is much slower than the timescales that were studied. Since surface diffusion is the dominant transport mechanism, the positive radius of curvature can be related to the time that the neck has been growing through a standard power law dependence (derived by assuming spherical particles and isotropic surface energies): x = [Kt] 1'7.
(2)
The value of the constant K is obtained from a regression of the data, and can be related to several system parameters as given below [16]:
56~R3yD~ds kbT
(c)
K-
(3)
Fig. 1. High-resolution still images taken from real-time videotape monitoring of the neck region between two ZrO 2 particles after: (a) 30 rain, (b) 60 rain, and (c) 90 min at (890 _+30)°C.
where f~ is the molar volume, R is the radius of the sintering particles (assumed to be spherical), 7 is the
J. Rankin, B.W. Sheldon / MateriaL~ Science and Engineerin¢ A204 (1995) 48 53
surface energy (assumed to be isotropic), c5s is the surface layer thickness, k b is Boltzman's constant, and T is the absolute temperature. By substituting appropriate values of 7, E2, R, ~5, ]¢b, and T in the equation above, the surface diffusion coefficient, D~, can be estimated; at 890°C it is found to be between 10 12 and 10-13 cm 2 s t. The second noteworthy phenomenon in the ZrO2 system is the fluctuations on the surfaces of these particles at ~ I I00°C. This phenomenon has been observed in ZrO2 [13] and in small gold particles [17]. Because of the nature of high-resolution T E M imaging, single atoms are not detectable, that is, the electron beam must pass through a minimum thickness of material (approximately 3 to 7 unit cells before imaging is possible). When cross-fringes are visible, the sample is oriented with the zone-axis parallel to the electron beam, in which case the T E M image is formed by the passage of the electron beam through columns of atoms which are parallel to the zone-axis. When part of a T E M image 'disappears' it indicates that less than a critical number of atoms remain in a particular column. Therefore, it is logical to conclude that the observed fluctuations arise from the motion or 'hopping' of clusters of atoms on and off of the surfaces of the particles. An example of this cluster motion can be seen in Figs. 2(a)-(c). Each number in Fig. 2 indicates the location of a different column of atoms. The column marked with a '1' is visible in Fig 2(a), but not visible in Fig 2(b), and is visible again in Fig 2(c). Similarly, the site marked with a '2' appears to be filled in Figs. 2(a) and (b), but is not visible in Fig. 2(c). A '3' marks the site where a column is not visible in Fig. 2(a), whereas this site appears to be filled in Fig. 2(b), and is not visible (along with the atoms in site '2') in Fig. 2(c). The images shown here are taken from a videotape of the in situ heating process, and span a time of approximately 5 s. Measurements from the videotape of the frequency of the motion of clusters on and off of the surface, together with a simplified random-walk calculation, Eq. (4) below, can be used to estimate a diffusion coefficient for this phenomenon. It should be noted that the oscillations observed here reflect the motion of columns of atoms, not the motion of individual atoms normally associated with a random-walk description of surface diffusion [18]: F D = ~ nr -.
51
(a)
~b)
(4)
The quantity F is the j u m p rate of the column of atoms, and is estimated to be ~ 2 s 1. The j u m p distance r is of the order of one lattice spacing ( ~ 0.4 nm), and the number of atoms per column n is probably between 10 and 100. Using these values, the diffusion coefficient is calculated as 2(10) 14 to 2(10) ~3 cm 2 S 1.
(c) Fig, 2. High-resolution still images taken from real-time videotape monitoring of the edge of a Z r O 2 particle. l-he total elapsed time between images (a) and (c) is ~ 5 seconds. The numbers in these images denote the location of columns of atoms which appear and disappear over the course of the experiment.
52
J. Rankin, B.W. Sheldon / Materials' Science and Engineering A204 (1995) 48 53
Recently Kusunoki et al. [12] have made in situ observations of nano-sized ZrO2 at l l00°C and have reported the occurrence of surface fluctuations (similar to those observed here). They have suggested that these fluctuations correspond to surface diffusion. However, D~ values obtained from the rate of neck growth (i.e. with Eq. (3)) are considerably larger than values obtained from the observed fluctuations (i.e. with Eq. (4)). It is important to note that the estimates made with Eqs. (3) and (4) are approximate, and are probably only accurate to within one or two orders of magnitude. However, the calculations made with Eq. (3) are based on neck growth rates that were measured at a lower temperature (890°C) than the surface fluctuation measurements (ll00°C), therefore the flux associated with neck growth is almost certainly much larger than the flux associated with surface fluctuations. Even though the observed rate of surface fluctuations is apparently too low to directly account for neck growth, the surface fluctuations are still probably related to surface mobilities. Instead of the traditional picture of individual atoms moving randomly along a relatively static surface, it appears that surface atoms can form clusters that essentially move as a unit. Additional studies are currently underway to elucidate this phenomenon. It should be noted that surface oscillations and reconstruction have been observed at both room temperature and elevated temperatures in other systems such as CdTe and CdS, where they have been attributed to electron beam-solid interactions at room temperature and thermal effects at higher temperatures [19,20]. Related studies [21] suggest that electron beam irradiation is responsible for enhanced atomic mobility and dislocation motion at lower temperatures, whereas at higher temperatures the dislocation velocities are thermally activated and exhibit standard Arrhenius-type behavior. In other studies, the electron beam has been shown to induce a room temperature reduction of irradiated surfaces of transition metal oxides to yield either the metal [22], or a lower oxide [23]. In those studies, the frequency of surface oscillation or phase transformation was found to be strongly dependent on the electron beam current and the time of exposure. For the results reported here the incident beam current was varied with no effect on the nature of the oscillations. Additionally, it should be noted that no oscillations are observed at temperatures less than ~ 1000°C even though, as previously discussed, neck growth via surface occurs at 890°C. These observations confirm that the oscillations are thermally induced.
4. Summary In situ TEM heating studies of Zr02 have provided new insights into the sintering process. Specifically, it
has been shown that: (1) Unconstrained, single-crystal particles of ZrO2 in contact with only one other particle reorient during heating at 890°C. (2) Neck growth during the early stages of sintering occurs at 890°C. However, at longer times, the necks reach a static size. This observation is in good agreement with the results of other researchers [4]. Measurements of the neck radius as a function of time are used to provide an estimate of the surface diffusion coefficient at this temperature. (3) Surface fluctuations are observed when ZrO~ particles are heated to temperatures greater than 1000°C. These fluctuations are associated with the motion of clusters of atoms, and do not appear to be direct evidence of 'traditional' surface diffusion. Additional experiments are essential if the origins and ramifications of cluster migration in this system are to be thoroughly understood.
Acknowledgments We wish to thank L.A. Boatner and A.F. Schwartzman for their valuable discussions and comments, and the National Science Foundation for providing the funding for this research.
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