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The effect of applied stress on densification of nanostructured zirconia during sinter-forging
August 1994
Materials Letters 20 ( 1994) 305-309
ELSEVIER
The effect of applied stress on densification of nanostructured zirconia during sinter-forging G. Skandan a, H. Hahn a,1,B.H. Kear a, M. Roddy b, W.R. Cannon b aDepartment ofMaterials Science and Engineering, Rutgers - The State University of New Jersey, Piscataway, NJ 08855, USA b Department of Ceramic Engineering, Rutgers - The State University ofNew Jersey, Piscataway, NJ 08855, US,4
Received 25 April 1994; accepted 29 April 1994
Abstract Nanoparticles of ZrOz (n-ZrO,) synthesized by the inert gas condensation technique were consolidated by sinter-forging, which is a pressure-assisted sintering process. It was found that there is a threshold stress below which there is only a small contribution to densification by the applied pressure. The value of the threshold stress depends on grain size and the effect is explained on the basis of driving forces for sintering. The grain size in the fully dense n-ZrOz samples was 45 nm.
1. Introduction Sinter-forging and hot-pressing of ceramics are often used as consolidation techniques when either materials are difficult to densify, a very fine microstructure is desired or consolidation at a low temperature ( = 0.5T,) is desired. These two consolidation processes are different in that in sinter-forging, the sample is not constrained in the lateral dimension. The mechanistics of this process have been studied by a number of different researchers [ l-3 1. In principle, sinter-forging can be applied to fabricate dense, net shape components as well as obtain the very line grain size nanocrystalline ceramics. Nevertheless, there is an effort to obtain finer grain sizes to optimize properties such as superplasticity. For example, it has been demonstrated by Hahn and Averback [ 41 that large strains ( ~0.6) can be obtained in compression with nanostructured ceramics (initial grain size= 14 nm) at low temperatures ( < 0.5 T,). ’ Present address: Technische Hochschule Darmstadt, Hilperstrasse 3 1.64295 Darmstadt, Germany.
It is thus important that the limits of sinter-forging of nanostructured ceramics be determined. Recently, sinter-forging has been employed to consolidate commercial powders, as well as nanoparticles. Owen and Chokshi [ 51 sinter-forged commercial 3 Y-TZP to near theoretical density at 1300°C under a stress of 20 MPa. The final grain size was 150 nm. Boutz et al. [ 6 ] achieved near theoretical densities by sinter-forging nanoparticles of 2.6 Y-TZP (primary particle size = 8 nm) at 1150°C for 25 min under an applied stress of 84 MPa. In all their experiments, the final density increased with increasing applied pressure. However, Hofler and Averback [ 7 ] found that for n-TiO,, below an applied stress of about 40 MPa (the threshold stress), there was no enhancement in densification due to the external pressure. Threshold stresses have not been reported previously for either hot pressing or hot forging and so it may be that they apply exclusively to nanocrystalline materials. It was suggested by Hofler and Averback [ 71 that grain rearrangement is very important in nanocrystalline materials and that the threshold stress is the necessary stress for grain boundary shear. They
0167-577x/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIO167-577x(94)00114-3
306
G.Skmdan et al. /Materials Letters 20 (1994) 305-309
proposed that grain rearrangement by sliding grains into vacant sites accounted for densitication and that a threshold stress must be obtained to allow sliding. This stress was estimated as the stress at which the external work done is enough to create the new surface area formed by sliding of grains past each other and obtained a value close to 40 MPa for the threshold stress. Generally, however, it is believed that the rearrangement stage is insignificant after the intermediate stage of sintering. The applied pressure, on the other hand, contributes towards the driving force for pore shrinkage during all stages of densification. Expe~ment~y, it should be possible to determine if the threshold stress is the stress to allow grains to slide past each other since the threshold stress would be independent of the grains size. Any dependence of the threshold stress on grain size should indicate that there is some other mechanism responsible for the observed threshold stress. In order to investigate the grain size dependence on the densification characteristics of ultrafinegrained ceramics under pressure, sinter-forging was carried out on compacts made from n-ZrOz powders with different initial particle sizes.
2. ExperimentaI procedure Nanoparticles of 210~ ( n-ZrOz) were synthesized by the inert gas condensation (IGC) technique described in detail elsewhere [ 8,9]. Essentially, the process consists of evaporating ZrG in an atmosphere of helium between 1 and 25 mbar in a UHV chamber. Nanoparticles of ZrG condense on the coldfinger and on the walls of the chamber. These are subsequently oxidized in situ to form nanoparticles of Zr02. Stoichiometric n-Zr& is obtained by annealing the powder at 350°C in an atmosphere of oxygen. An important variable controlling the average particle size is the helium gas pressure inside the chamber. Powders with different average particle sizes were obtained by varying the pressure of the inert gas in the chamber. Green pellets, 5 mm in diameter and 3 mm thick, were made by cold isostatic pressing at 40 ksi. These were partially sintered at 700°C for 5 min to improve the strength. The pellets were then subjected to a compressive stress in a creep rig. All the tests were
carried out at constant load. The axial strain of the sample was measured by a three-point extensometer coupled to an LVDT. The LVDT was calibrated for an expansion range of 0.1 inch with an accuracy of 0.1%. The initial applied stress ranged from 10 to 300 MPa. The forging temperature was 950°C. Both the heating and cooling rates were lO”C/min. The load was applied once the set temperature was reached. The holding time was varied between 2.5 and 180 min. An isothermal series of tests at 950°C and an applied pressure of 100 MPa were also performed to examine the effect of time on densification. The bulk density was measured using Archimedes principle and the grain size was determined from X-ray line broadening. There were also control samples which were subjected to the same heating schedules, but without an applied load.
3. Results and discussion Powders with average particle sizes (determined from bright-field TEM images) of 6 nm (powder A) and 12 nm (powder B) were obtained by evaporating at 2.75 and 20 mbar, respectively. Powder A had a specific surface area of 136 m*/g while the corresponding value for powder B was 65 m*fg. Green densities between 45 and 5O*hof the theoretical value were obtained after CIPing the powders. Fig. 1 shows a curve of relative density as a function of time for an applied stress of 100 MPa at a temperature of 950°C. There is almost no improvement in density for time periods beyond 60 min. Fig. 2 shows a curve of relative density as a function of applied stress. The densities of the control samples, that is those subjected to no load but only temperature for 180 min, for powders A and B were 83.1 and 67% of theoretical density, respectively. With powder A, which is the line grained material, for stresses below 35 MPa, there is only a marginal enhancement in density due to pressure. Above this stress level, the applied pressure contributed significantly to densi~cation. Densities in excess of 99.5% were achieved by applying a pressure of 300 MPa. The total axial strain at this load was approximately 30%. The distinct break in the curve is evident in Fig. 2. A similar break was also observed with powder B, but at a lower stress ( = 15 MPa). Thus the break in
307
G. Skandan et al. /Materials Letters20 (1994) 305-309
force due to curvature and the other due to the applied stress [ 10,111. The type of equation which describes this is as follows: DF = y!X+ gP, ,
70
I 0
100
200
Forging time (min.)
Fig. 1. Relative density as a function of holding time for an initial applied pressure of 100 MPa at a temperature of 950°C. There is no appreciable improvement in density for holding periods greater than 1 h. 100
,
I
(1)
where DF is the driving force for densitication, y is the surface energy, 52 is the molecular volume, K is proportional to the curvature of the shrinking “pore” which in turn is approximately inversely proportional to the grain size, g is a geometrical constant and Pa is the applied pressure. Thus only the first term on the right hand side of Eq. ( 1) has a grain size dependence. In different stages of sintering, the specifics of this equation change but the form remains the same. Fig. 3 shows a schematic of the driving force as a function of grain size. At small grain sizes, such as Gl, the contribution of the applied stress to the total driving force is far less significant as compared to that due to the surface area. At a grain size G2, the two components are comparable while at G3, stress plays a dominant role. The threshold stress is the stress at which the driving forces are equal, Pa = ySZKlg .
_.
(2)
On the basis of this argument, one can expect to have a break in a curve of densification rate versus applied stress. Since the final density is a consequence of the densitication rate. the break in the curves for the difi
80
/
1
/
IllI,’ 10
j
I’I
[_)) 11111,
I
100
1
I
I”“1 1000
Applied Pressure (MPa) Fig. 2. Relative density as a function of applied stress for samples prepared from powder A and powder B. The holding time was 180 min. The data for 1 MPa are from the control samples which were subjected to the same holding time but without any load.
the curve appears to be dependent on the initial particle size. More precisely, the threshold stress is a function of the grain size at the time of application of load, once the forging temperature has been reached. The grain size for the control sample with powder A was 35 nm while that with powder I3 was 55 nm. This result can be interpreted by considering the driving force for densitication. The total driving force is composed of two components; the intrinsic driving
10
100
1000
Chain size (mn)
Fig. 3. Schematic of the driving forces for sintering: the total driving force is composed of an intrinsic driving force for sintering (due to curvature) and an extrinsic driving force (due to the applied pressure). At small grain sizes the former has a dominant effect and vice-versa.
G. Skmtdan et al. / Maie~i~s Letters 20 (I994) 305-309
308
ferent grain sized materials occur at different stress levels. Fig. 4 shows grain size (calculated from X-ray line broadening [ 121) as a function of applied stress for the fine grained material. The slope of the line is positive. It is not clear if this grain growth is static grain growth occurring concurrently with densification or if it is a dynamic grain growth occurring due to increasing applied stress. The grain size in the fully sintered state (from powder A) from line broadening measurements was found to be 45 nm. It should be noted that the stresses used in these experiments to achieve full density are significantly higher than that employed with commercial grade submicron powders. At a stress of 100 MPa, nanoparticles can be sinter-forged to full density only at a temperature around 1000°C. Thus there is only a 100 degree reduction in sintering temperature as compared to free sintering in air [ 9 1. This could be due to the fact that the diffusivity varies exponentially with tem~rature and so the diffusivity at temperatures such as 950°C is very low. Conversely, a very high pressure is required to sinter-forge n-zirconia at temperatures lower than 950°C. This means that for nanostructured powders which have a large intrinsic driving force (i.e. high surface area), very high pressures will be required to have additional benefit from pressure-assisted sintering techniques such as hotpressing and sinter-forging. This is illustrated in Fig. 5 where the threshold stress is plotted as a function
‘0
1 10
Grain size (nm)
100
Fig. 5. Threshold stress as a function of gram size of the control samples. At grain sizes below 25 nm or so, the threshold stress is expected to be very high ( = 100 MPa) whereas at grain sizes in the submicron range, there should be no threshold stress. This is indeed the case as a threshold stress has never been observed in commercial materials.
of grain size of the control samples. Although insufficient data are available to accurately determine the proper factions relations~p, Fig. 5 shows that at grain sizes above 100 nm, i.e. in micrograined materials, the threshold stress is too small to be observed and that a very large threshold stress may exist below 10 nm. In an earlier work it was shown that the sintering temperatures and hence final grain size can be reduced by sintering in vacuum [ 9 3. This can be extrapolated to predict that grain sizes can be further reduced by sinter-forging in vacuum.
4. Conclusions
0
100
200
300
400
Appliedpressun:(MPa) Fig. 4. Grain size (calculated from X-my line broadening) as a function of applied stress for samples from powder A, which is the finer grained material.
(i) Sinter-forging can be used as a processing technique to densify nanoparticles of oxides and simultaneously preserve the nanoscale structure. (ii) Densities in excess of 99% were obtained in sinter-forged pellets of nanostructured zirconia. The tinal grain size in the fully sintered material was 45 nm. (iii) The threshold stress is a function of the initial particle size and more so, is a function of the grain size at the time of application of load.
G. Skandan et al. /Materials Letters20 (1994) 305-309
References [ 11 M.N. Rahaman, L.C. De Jonghe and C.H. Hsueh, J. Am. Ceram. Sot. 69 (1986) 58. [2] P.C. Panda, J. Wang and R. Raj, J. Am. Ceram. Sot. 7 1 (1988) C-507. [3] K. Venkatachari and R. Raj, J. Am. Ceram. Sot. 69 ( 1986) 499. [4] H. Hahn and R.S. Averback, Nanostruct. Mater. 1 (1992) 95. [ 51D.M. Owen and A.H. Chokshi, Nanostruct. Mater. 2 (1993) 181.
309
[6] M. Boutz, A. Winnubst, A. Burggraaf, M. Nauer and C. Carry, in: Proceedings of zirconia V, the Fifth International Conference on the Science and Technology of Zirconia (1992). [7] H.J. Hofler and R.S. Averback, Proc. Mater. Res. Sot. 286 (1992) 9. [ 81 H. Hahn, Nanostruct. Mater. 2 ( 1993) 25 1. [ 9 ] G. Skandan, H. Hahn, M. Roddy and W.R. Cannon, J. Am. Ceram. Sot., in press. [ 101 J. Philibert, Atomic movements, diffusion and mass transport in solids (Les Editions de Physique, Paris, 199 1) . [ 1 l] R.L. Coble, J. ofApp. Phys. 41 (1970) 4798. [ 121 B.D. Cullity, Elements of X-ray diffraction, 2nd Ed. ( 1977).
Materials Letters 20 ( 1994) 305-309
ELSEVIER
The effect of applied stress on densification of nanostructured zirconia during sinter-forging G. Skandan a, H. Hahn a,1,B.H. Kear a, M. Roddy b, W.R. Cannon b aDepartment ofMaterials Science and Engineering, Rutgers - The State University of New Jersey, Piscataway, NJ 08855, USA b Department of Ceramic Engineering, Rutgers - The State University ofNew Jersey, Piscataway, NJ 08855, US,4
Received 25 April 1994; accepted 29 April 1994
Abstract Nanoparticles of ZrOz (n-ZrO,) synthesized by the inert gas condensation technique were consolidated by sinter-forging, which is a pressure-assisted sintering process. It was found that there is a threshold stress below which there is only a small contribution to densification by the applied pressure. The value of the threshold stress depends on grain size and the effect is explained on the basis of driving forces for sintering. The grain size in the fully dense n-ZrOz samples was 45 nm.
1. Introduction Sinter-forging and hot-pressing of ceramics are often used as consolidation techniques when either materials are difficult to densify, a very fine microstructure is desired or consolidation at a low temperature ( = 0.5T,) is desired. These two consolidation processes are different in that in sinter-forging, the sample is not constrained in the lateral dimension. The mechanistics of this process have been studied by a number of different researchers [ l-3 1. In principle, sinter-forging can be applied to fabricate dense, net shape components as well as obtain the very line grain size nanocrystalline ceramics. Nevertheless, there is an effort to obtain finer grain sizes to optimize properties such as superplasticity. For example, it has been demonstrated by Hahn and Averback [ 41 that large strains ( ~0.6) can be obtained in compression with nanostructured ceramics (initial grain size= 14 nm) at low temperatures ( < 0.5 T,). ’ Present address: Technische Hochschule Darmstadt, Hilperstrasse 3 1.64295 Darmstadt, Germany.
It is thus important that the limits of sinter-forging of nanostructured ceramics be determined. Recently, sinter-forging has been employed to consolidate commercial powders, as well as nanoparticles. Owen and Chokshi [ 51 sinter-forged commercial 3 Y-TZP to near theoretical density at 1300°C under a stress of 20 MPa. The final grain size was 150 nm. Boutz et al. [ 6 ] achieved near theoretical densities by sinter-forging nanoparticles of 2.6 Y-TZP (primary particle size = 8 nm) at 1150°C for 25 min under an applied stress of 84 MPa. In all their experiments, the final density increased with increasing applied pressure. However, Hofler and Averback [ 7 ] found that for n-TiO,, below an applied stress of about 40 MPa (the threshold stress), there was no enhancement in densification due to the external pressure. Threshold stresses have not been reported previously for either hot pressing or hot forging and so it may be that they apply exclusively to nanocrystalline materials. It was suggested by Hofler and Averback [ 71 that grain rearrangement is very important in nanocrystalline materials and that the threshold stress is the necessary stress for grain boundary shear. They
0167-577x/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIO167-577x(94)00114-3
306
G.Skmdan et al. /Materials Letters 20 (1994) 305-309
proposed that grain rearrangement by sliding grains into vacant sites accounted for densitication and that a threshold stress must be obtained to allow sliding. This stress was estimated as the stress at which the external work done is enough to create the new surface area formed by sliding of grains past each other and obtained a value close to 40 MPa for the threshold stress. Generally, however, it is believed that the rearrangement stage is insignificant after the intermediate stage of sintering. The applied pressure, on the other hand, contributes towards the driving force for pore shrinkage during all stages of densification. Expe~ment~y, it should be possible to determine if the threshold stress is the stress to allow grains to slide past each other since the threshold stress would be independent of the grains size. Any dependence of the threshold stress on grain size should indicate that there is some other mechanism responsible for the observed threshold stress. In order to investigate the grain size dependence on the densification characteristics of ultrafinegrained ceramics under pressure, sinter-forging was carried out on compacts made from n-ZrOz powders with different initial particle sizes.
2. ExperimentaI procedure Nanoparticles of 210~ ( n-ZrOz) were synthesized by the inert gas condensation (IGC) technique described in detail elsewhere [ 8,9]. Essentially, the process consists of evaporating ZrG in an atmosphere of helium between 1 and 25 mbar in a UHV chamber. Nanoparticles of ZrG condense on the coldfinger and on the walls of the chamber. These are subsequently oxidized in situ to form nanoparticles of Zr02. Stoichiometric n-Zr& is obtained by annealing the powder at 350°C in an atmosphere of oxygen. An important variable controlling the average particle size is the helium gas pressure inside the chamber. Powders with different average particle sizes were obtained by varying the pressure of the inert gas in the chamber. Green pellets, 5 mm in diameter and 3 mm thick, were made by cold isostatic pressing at 40 ksi. These were partially sintered at 700°C for 5 min to improve the strength. The pellets were then subjected to a compressive stress in a creep rig. All the tests were
carried out at constant load. The axial strain of the sample was measured by a three-point extensometer coupled to an LVDT. The LVDT was calibrated for an expansion range of 0.1 inch with an accuracy of 0.1%. The initial applied stress ranged from 10 to 300 MPa. The forging temperature was 950°C. Both the heating and cooling rates were lO”C/min. The load was applied once the set temperature was reached. The holding time was varied between 2.5 and 180 min. An isothermal series of tests at 950°C and an applied pressure of 100 MPa were also performed to examine the effect of time on densification. The bulk density was measured using Archimedes principle and the grain size was determined from X-ray line broadening. There were also control samples which were subjected to the same heating schedules, but without an applied load.
3. Results and discussion Powders with average particle sizes (determined from bright-field TEM images) of 6 nm (powder A) and 12 nm (powder B) were obtained by evaporating at 2.75 and 20 mbar, respectively. Powder A had a specific surface area of 136 m*/g while the corresponding value for powder B was 65 m*fg. Green densities between 45 and 5O*hof the theoretical value were obtained after CIPing the powders. Fig. 1 shows a curve of relative density as a function of time for an applied stress of 100 MPa at a temperature of 950°C. There is almost no improvement in density for time periods beyond 60 min. Fig. 2 shows a curve of relative density as a function of applied stress. The densities of the control samples, that is those subjected to no load but only temperature for 180 min, for powders A and B were 83.1 and 67% of theoretical density, respectively. With powder A, which is the line grained material, for stresses below 35 MPa, there is only a marginal enhancement in density due to pressure. Above this stress level, the applied pressure contributed significantly to densi~cation. Densities in excess of 99.5% were achieved by applying a pressure of 300 MPa. The total axial strain at this load was approximately 30%. The distinct break in the curve is evident in Fig. 2. A similar break was also observed with powder B, but at a lower stress ( = 15 MPa). Thus the break in
307
G. Skandan et al. /Materials Letters20 (1994) 305-309
force due to curvature and the other due to the applied stress [ 10,111. The type of equation which describes this is as follows: DF = y!X+ gP, ,
70
I 0
100
200
Forging time (min.)
Fig. 1. Relative density as a function of holding time for an initial applied pressure of 100 MPa at a temperature of 950°C. There is no appreciable improvement in density for holding periods greater than 1 h. 100
,
I
(1)
where DF is the driving force for densitication, y is the surface energy, 52 is the molecular volume, K is proportional to the curvature of the shrinking “pore” which in turn is approximately inversely proportional to the grain size, g is a geometrical constant and Pa is the applied pressure. Thus only the first term on the right hand side of Eq. ( 1) has a grain size dependence. In different stages of sintering, the specifics of this equation change but the form remains the same. Fig. 3 shows a schematic of the driving force as a function of grain size. At small grain sizes, such as Gl, the contribution of the applied stress to the total driving force is far less significant as compared to that due to the surface area. At a grain size G2, the two components are comparable while at G3, stress plays a dominant role. The threshold stress is the stress at which the driving forces are equal, Pa = ySZKlg .
_.
(2)
On the basis of this argument, one can expect to have a break in a curve of densification rate versus applied stress. Since the final density is a consequence of the densitication rate. the break in the curves for the difi
80
/
1
/
IllI,’ 10
j
I’I
[_)) 11111,
I
100
1
I
I”“1 1000
Applied Pressure (MPa) Fig. 2. Relative density as a function of applied stress for samples prepared from powder A and powder B. The holding time was 180 min. The data for 1 MPa are from the control samples which were subjected to the same holding time but without any load.
the curve appears to be dependent on the initial particle size. More precisely, the threshold stress is a function of the grain size at the time of application of load, once the forging temperature has been reached. The grain size for the control sample with powder A was 35 nm while that with powder I3 was 55 nm. This result can be interpreted by considering the driving force for densitication. The total driving force is composed of two components; the intrinsic driving
10
100
1000
Chain size (mn)
Fig. 3. Schematic of the driving forces for sintering: the total driving force is composed of an intrinsic driving force for sintering (due to curvature) and an extrinsic driving force (due to the applied pressure). At small grain sizes the former has a dominant effect and vice-versa.
G. Skmtdan et al. / Maie~i~s Letters 20 (I994) 305-309
308
ferent grain sized materials occur at different stress levels. Fig. 4 shows grain size (calculated from X-ray line broadening [ 121) as a function of applied stress for the fine grained material. The slope of the line is positive. It is not clear if this grain growth is static grain growth occurring concurrently with densification or if it is a dynamic grain growth occurring due to increasing applied stress. The grain size in the fully sintered state (from powder A) from line broadening measurements was found to be 45 nm. It should be noted that the stresses used in these experiments to achieve full density are significantly higher than that employed with commercial grade submicron powders. At a stress of 100 MPa, nanoparticles can be sinter-forged to full density only at a temperature around 1000°C. Thus there is only a 100 degree reduction in sintering temperature as compared to free sintering in air [ 9 1. This could be due to the fact that the diffusivity varies exponentially with tem~rature and so the diffusivity at temperatures such as 950°C is very low. Conversely, a very high pressure is required to sinter-forge n-zirconia at temperatures lower than 950°C. This means that for nanostructured powders which have a large intrinsic driving force (i.e. high surface area), very high pressures will be required to have additional benefit from pressure-assisted sintering techniques such as hotpressing and sinter-forging. This is illustrated in Fig. 5 where the threshold stress is plotted as a function
‘0
1 10
Grain size (nm)
100
Fig. 5. Threshold stress as a function of gram size of the control samples. At grain sizes below 25 nm or so, the threshold stress is expected to be very high ( = 100 MPa) whereas at grain sizes in the submicron range, there should be no threshold stress. This is indeed the case as a threshold stress has never been observed in commercial materials.
of grain size of the control samples. Although insufficient data are available to accurately determine the proper factions relations~p, Fig. 5 shows that at grain sizes above 100 nm, i.e. in micrograined materials, the threshold stress is too small to be observed and that a very large threshold stress may exist below 10 nm. In an earlier work it was shown that the sintering temperatures and hence final grain size can be reduced by sintering in vacuum [ 9 3. This can be extrapolated to predict that grain sizes can be further reduced by sinter-forging in vacuum.
4. Conclusions
0
100
200
300
400
Appliedpressun:(MPa) Fig. 4. Grain size (calculated from X-my line broadening) as a function of applied stress for samples from powder A, which is the finer grained material.
(i) Sinter-forging can be used as a processing technique to densify nanoparticles of oxides and simultaneously preserve the nanoscale structure. (ii) Densities in excess of 99% were obtained in sinter-forged pellets of nanostructured zirconia. The tinal grain size in the fully sintered material was 45 nm. (iii) The threshold stress is a function of the initial particle size and more so, is a function of the grain size at the time of application of load.
G. Skandan et al. /Materials Letters20 (1994) 305-309
References [ 11 M.N. Rahaman, L.C. De Jonghe and C.H. Hsueh, J. Am. Ceram. Sot. 69 (1986) 58. [2] P.C. Panda, J. Wang and R. Raj, J. Am. Ceram. Sot. 7 1 (1988) C-507. [3] K. Venkatachari and R. Raj, J. Am. Ceram. Sot. 69 ( 1986) 499. [4] H. Hahn and R.S. Averback, Nanostruct. Mater. 1 (1992) 95. [ 51D.M. Owen and A.H. Chokshi, Nanostruct. Mater. 2 (1993) 181.
309
[6] M. Boutz, A. Winnubst, A. Burggraaf, M. Nauer and C. Carry, in: Proceedings of zirconia V, the Fifth International Conference on the Science and Technology of Zirconia (1992). [7] H.J. Hofler and R.S. Averback, Proc. Mater. Res. Sot. 286 (1992) 9. [ 81 H. Hahn, Nanostruct. Mater. 2 ( 1993) 25 1. [ 9 ] G. Skandan, H. Hahn, M. Roddy and W.R. Cannon, J. Am. Ceram. Sot., in press. [ 101 J. Philibert, Atomic movements, diffusion and mass transport in solids (Les Editions de Physique, Paris, 199 1) . [ 1 l] R.L. Coble, J. ofApp. Phys. 41 (1970) 4798. [ 121 B.D. Cullity, Elements of X-ray diffraction, 2nd Ed. ( 1977).