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The kinetics of grain growth in nanocrystalline copper
Scripta METALLURGICA et M A T E R I A L I A
Vol.
25, pp. 2 6 9 9 - 2 7 0 4 , 1991 P r i n t e d in the U . S . A .
Pergamon Press plc All rights reserved
THE KINETICS OF GRAIN GROWTH IN NANOCRYSTALLINE COPPER
S.K. Ganapathi +, D.M. Owen* and A.H. Chokshi* +Center for Magnetic Recording Research *Department of Applied Mechanics and Engineering Sciences University of California, San Diego La Jolla, CA 92093 ( R e c e i v e d A u g u s t 26, 1991) (Revised September 24, 1991)
i. Introduction A decrease in grain size from the micrometer to the nanocrystalline range leads to a significant increase in the fraction of atoms residing at grain boundaries. There has been considerable research activity recently in developing and characterizing nanocrystalline materials in bulk form, as noted in recent reviews on the topic [1-3]. Following the pioneering study by Gleiter [4] to form nanocrystalline metals by an inert gas condensation method [4,5], nanocrystalline materials have also been formed by high energy ball milling [6,7], sliding wear [8] and chemical synthesis techniques [9,10]. Experimental results suggest that nanocrystalline materials may exhibit different physical and mechanical properties from conventional polycrystalline materials. One of the interesting applications for nanocrystalline materials is in superplastic forming. It has been noted that the optimum strain rate for superplasticity (iopt) scales inversely with the grain size (d) as follows: ~^_~ ~ d'q where the exponent q has a value between -2 and 3 [ii]. It is necessary to limit grain growth during the consolidation of nanocrystalline powders to form bulk products, in order to fully exploit the potential superplastic and other structural capabilities of these materials. Early studies indicated that nanocrystalline materials have a remarkable resistance to grain growth. Thus, for example, no grain growth was observed in Cu with a grain size of 8 nm after annealing for 60 hours at 393 K [12]. Subsequent studies on nanocrystalline ceramics confirmed these results, and it was shown that there was very little grain growth below a critical temperature [5,13,14]. Eastman e_!ta_!. [14] attributed the stability of nanocrystalline materials to the narrow grain size distributions in these materials. One of the major limitations of these studies on grain growth is that they were conducted on bulk compacted nanocrystalline materials with a significant level of porosity, ranging from i0 to 25%. It is well known that pores may hinder grain growth during sintering [15]. Hofler and Averback [16] demonstrated recently that a decrease in porosity from 25% to 10% in nanocrystalline TiO 2 can lead to a substantial increase in the grain size after annealing. These results suggest that the intrinsic grain growth characteristics of nanocrystalline materials, in the absence of porosity, may be substantially different from those in porous compacts. To date, these results on somewhat porous TiO 2 are the only published data available on determining the kinetics of grain growth in nanocrystalline materials. Normal grain growth in polycrystalline materials is related to a time invariant form of the grain size distribution [17], so that a simple normalization procedure will enable the superimposition of the distributions at two different time intervals. On the other hand, abnormal grain growth leads to a broadening of the grain size distribution by the growth of a few large grains. Siegel et al. [5] noted that an as-compacted (porous) nanocrystalline TiO 2 appeared to exhibit a log-normal grain size distribution. It is not clear whether fully dense nanocrystalline materials exhibit a log-normal distribution and normal grain growth characteristics.
2699 0036-9748/91 $ 3 . 0 0 + .00 Copyright (c) 1 9 9 1 P e r g a m o n P r e s s
plc
2700
NANOCRYSTALLINE
Cu
The kinetics of normal grain growth in polycrystalline represented by an equation of the following form:
Vol.
25,
No.
materials are usually
dN-d~ -Kt
(i)
where d o is the initial grain size, d is the grain size after annealing for a time period of t, and K and N are constants. Various theories for grain growth lead to values of the exponent N from 1 to 4 [17]. The kinetic constant K may be represented as: KzK o exp(-Q/RT)
(2)
where K o is a constant, Q is the activation energy, R is the gas constant and T is the absolute temperature. Experimental studies on grain growth are usually designed to evaluate the values of N and Q, and to determine the mechanism for grain growth by comparing the experimental values with theoretical predictions. The present investigation was undertaken to characterize the grain growth behavior of nanocrystalline materials in the absence of porosity, with the following two specific objectives: (i) to examine whether such materials display normal grain growth, and (ii) to evaluate the grain growth kinetic exponent N and activation energy Q. 2. Experimental Material and Procedures The nanocrystalline material used in the present investigation was obtained by a process of sliding wear [18]. A stainless steel ring was mounted on a shaft and rotated while in contact with an OFHC copper block under a constant load. The debris was typically in the form of thin flakes with an average thickness of -0.5 ~m, and it was found to consist predominantly of Cu with -0.8% Fe and a thin layer of copper oxide on the surface. A transmission electron microscopy (TEM) study revealed that the wear debris was nanocrystalline with grain sizes ranging from 2 to 30 um [19]. In addition, it was also noted that the wear debris exhibited a slight crystallographic texture [18]. For the present experiments, all of the copper debris was initially annealed for 7 minutes at 473 K in hydrogen to reduce the oxide layers on the surfaces. Investigation by bright field TEM revealed the absence of porosity in the wear debris. The wear debris was ideally suited for the present investigation, because the particles were fully dense and it was therefore possible to study grain growth in nanocrystalline copper, in the absence of porosity. For the grain growth study, the debris was encapsulated in quartz tubes which were evacuated and then sealed. Different vials were then annealed at 575, 625 and 675 K for periods of I, 4 and 20 hours. The annealed, powders were mixed with acetone and treated in an ultrasonic bath to break up loose agglomerates and separate the particles. The powder suspension was then sprayed on to a carbon film deposited on a mica substrate, picked up on a 200 mesh copper grid and examined by TEM. The debris particles were thin enough to be electron transparent. The annealed powders were examined at 300 kV in a Philips CM30 TEM. A series of dark field images was obtained from all the annealed specimens by placing the objective aperture over a section of the (Iii) diffraction rings. The grain size distributions were characterized from these micrographs using a video image analysis system connected to a personal computer. A sufficient number of measurements were recorded to minimize errors in determining the grain size. 3, Experimental Results The transmission electron microscopy investigation revealed that the individual particle sizes were similar before and after annealing, thereby indicating the absence of significant sintering and agglomeration. Measurements indicated that the average initial grain size was 18±1.1 nm, prior to annealing the specimens for the grain growth study. The largest linear dimensions of the crystallites were recorded from the micrographs, and some of the typical experimental results are shown in Fig. i in the form of histograms
12
Vol.
25, No.
12
NANOCRYSTALLINE
Cu
2701
depicting the size distribution of crystallites after i and 20 hours of annealing at 625 K. The histograms suggest that the grain sizes follow a log-normal distribution. All of the experimental results obtained in the present investigation are summarized in Fig. 2, which shows the variation in average grain size with annealing time at three different temperatures. The error bars on the datum points tend to be in the range of ~I0% error at the 95% confidence limit. The results shown in Fig. 2 indicate that the largest average grain size achieved in the present study was -55 nm after annealing for 20 hours at 675 K.
40
2O Cu
Nanocrystalline
>
T = 625 K t = 3.6x103
30
d =
>,
T = 625 K t = 7.2x104
15
s
22.6±1.1
Cu
Nanocrystalline
nm
o"
~ 2c
lO
u.
U.
s
5 @
n" m
25
0
75
50 cl i
100
125
150
0
25
75
50 di
(nrn)
(a)
100
125
150
(nm)
(b)
Fig. I Histograms showing size distribution of nanocrystalline Cu grains after annealing at 625 K for (a) I hour and (b) 20 hours.
70
I
I
I
I
I
I
I
I
I
Nanocrystalline Cu [] initial
T~
T (K) 50
A 625
E v
/
~
c
-0
30
10
I
0
Fig. 2
I
I
20
I
I
I
40 3 10 t (s)
I
I
60
Variation in average grain size with annealing time and temperature.
I
80
2702
NANOCRYSTALLINE
Cu
Vol.
25,
No.
4. Discussion 4,1 The Validity of the Present Experimental Results It is necessary to evaluate the possibility that the present experimental results were influenced by the small sizes of the debris particles (-0.5 ~m). As noted by Thompson [20] in a review of grain growth in thin films, grain growth in an equiaxed structure in thin films occurs in a manner similar to that in bulk polycrystalline materials until the grains grow to dimensions equal to the film thickness. Even at the coarsest grain sizes encountered in this study, there were likely to be more than -4 to 5 grains across the thickness of the particles. Consequently, the present results are not likely to have been influenced by the fine sizes of the debris. The grain sizes in nanoerystalline materials have been estimated from x-ray diffraction peak broadening techniques [6,7,21,22] or determined directly by TEM [5,12,23]. Nieman and Weertman [22] conducted a detailed investigation to determine grain sizes by x-ray diffraction, and they concluded that the errors in the measurements are of the order of K25% and KI00% for grain sizes of K25 nm and k50 nm, respectively. In view of these relatively large errors, the direct measurements recorded in the present investigation are preferable due to the smaller errors of s10%. In addition, the large strains associated with the wear debris are likely to increase the errors in grain size determination by x-ray diffraction. The nanocrystalline materials generally produce a ring diffraction pattern in TEM studies. A portion of the ring is utilized in producing the dark field images used for grain size measurements. With the smallest aperture available, simple calculations indicate that the present technique is not capable of distinguishing between adjacent grains if their misorientations are ~5 ° . However, since grain growth proceeds largely by the migration of high angle grain boundaries, the above difficulty is not a serious limitation. Finally, it is important to note that nanocrystalline materials produced by different techniques may lead to variations in mechanical characteristics. Thus, for example, Mayo [24] has demonstrated recently that nanocrystalline Cu produced by the inert gas atomization technique and by the sliding wear process exhibit substantially different hardness characteristics, in spite of their nominally similar grain sizes. 4.2 The Characteristics of Grain Growth Normal grain growth is characterized by a time invariant shape of size distribution; normalizing the distributions by the respective average grain sizes will lead to the superimposition of the distributions at different time i
),
99.9 99
o
E
•
D
~LL .> E
O
90 70 50 3O 10
i
i
i
i
i
I
NanocrystallineT = 6 2 5 K Cu t (s)
A J
d (nm)
^
44.~
o 3600
2Z--Z
A 14400 72000
33.2
n
1
0.1 I
I
i
|
i
i
I
0.1
I
|
1.0
5.0
dild Fig. 3 Cumulative probability vs normalized grain size for the nanocrystalline Cu annealed at 625 K for i, 4 and 20 hours: size distributions are normalized by average grain sizes.
12
Vol.
25,
No.
12
NANOCRYSTALLINE
Cu
2703
intervals. The present experimental results were tested for this behavior by plotting the results in the form shown in Fig. 3: on such a plot, a log-normal distribution will lead to the data falling on a straight line. Inspection of the experimental results shown for grain growth at 625 K indicate that the data for three different annealing times fall essentially on a single straight line, thereby confirming the occurrence of normal grain growth in the nanocrystalline material with a log-normal distribution. Similar results were obtained at the two other temperatures used in this investigation. Hillert [25] has examined theoretically the conditions necessary for the onset of abnormal grain growth, and concluded that abnormal grain growth is likely when the ratio of largest grain size to average grain size, dmax/d, in a material is >2. Brook [26] noted qualitatively that a ratio of dmax/d >2.5 to 3 is necessary for abnormal grain growth. The experimental results in the present study indicate that normal grain growth occurs in spite of the ratio dmax/d being ~3. A similar result was noted in an earlier study on static grain growth in a ZRO2-20% AI203 composite [27]. These experimental observations are consistent with the computer simulations of Srolovitz et al. [28] which indicate that the presence of grains significantly larger than the average value does not necessarily lead to abnormal growth. Thompson e__tta l. [29] obtained a similar result analytically, and this was extended by Rollett et al. [30] to include anisotropies in grain boundary mobilities. 4.3 The Kinetics of Grain Growth The correlation coefficients, r, were evaluated for values of N equal to 2, 3 and 4 in eqn. I, to determine the appropriate grain growth exponent. The experimental results for the three different temperatures indicated that there was very little difference in r for the different exponents. Thus, calculations at 625 K indicated that the values of r are 0.96, 0.99 and 1.0 for N=2, 3 and 4, respectively. A similar evaluation of the exponent N, using the data reported for porous nanocrystalline TiO 2 by Hofler and Averbach [16], indicated that the values of r are -0.98, 0.98 and 0.97 for N-2, 3 and 4, respectively. Very similar results were obtained in an earlier study on static grain growth of fully dense microduplex ZRO2-20% AI203 composite [27]. The relatively minor differences in the correlation coefficients obtained are not necessarily related to the small statistical sample size. Thus, for example, a re-evaluation of data on grain growth in high purity Cd [31] with 17 datum points indicated that the values of r are 0.98, 0.98 and 0.95 for N-2, 3 and 4, respectively: the data had been analyzed originally only in terms of N~2 [31]. The present analysis indicates that it is difficult to identify a grain growth mechanism on the basis of the exponent N. Also, as noted by Atkinson [17], several different mechanisms may be contributing to commonly reported exponents such as N=3. The activation energy for grain growth may be calculated using eqns. i and 2 with an appropriate value of N. Using N=4 for the present experimental results, the activation energy for grain growth was calculated to be 30±9 kJ mol -I. This value is much smaller than that reported (-80 kJ mol -I) for grain growth in polyerystalline Cu [32]. An activation energy of -i00 kJ mol "I (-0.5 Q~, where Q~ is the activation energy for lattice diffusion) is usually accepted as the value for grain boundary diffusion in polycrystalline copper, and the present activation energy is much smaller than the values reported in coarser grained polycrystalline Cu [33]. The large stored energy of cold work associated with sliding wear may have contributed to the low activation energy obtained in this investigation. Horvath e t a l. [12] and Schumacher et al. [34] determined the coefficients for diffusion in nanocrystalline Cu, with a relative density of -90%, for Cu and Ag, respectively: activation energies in the range of 38 to 66 kJ mol "I were reported. It is important to note that the diffusion data in nanocrystalline copper were obtained at a lower temperature range of 293 to 393 K in comparison with the temperature range of 575 to 675 K used in the present investigation. Additionally, it has been suggested that the lower activation energies obtained in nanocrystalline Cu [12,34] were a consequence of the porous nature of the specimens used in those investigations [35]. 5.
Summary and Conclusions
Grain growth in nanocrystalline copper was studied in the absence of porosity using wear debris obtained from sliding wear experiments. The results demonstrate for the first
2704
NANOCRYSTALLINE
Cu
Vol.
25,
No.
time that grain growth in nanocrystalline materials occurs in a normal manner, so that the log-normal form of the grain size distribution curve is not altered during grain growth. The analysis indicates that it is generally difficult to evaluate a grain growth exponent N, because very similar correlation coefficients are obtained with N values of 2, 3 and 4. The analysis also yielded a rather low value of activation energy for grain growth. Acknowledgement This work was supported in part by ARO under contract no. DAAL86-K-0169 and the National Science Foundation under Grant no. DMR-9023699. The authors are grateful to Dr. D.A. Rigney of Ohio State University for assistance in obtaining the Cu powders. References i. 2. 3. 4.
5. 6. 7. 8. 9.
i0. ii. 12. 13. 14.
15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.
R. Birringer and H. Cleiter, Encyclopedia of Materials Science and Engineering, vol. l-suppl. (edited by R.W. Cahn), p. 339, Pergamon Press, New York (1988). R.W. Siegel, MRS Bull., vol. XV, p. 60 (October 1990). H. Cleiter, Prog. Mater. Sci. 33, 223 (1990). H. Gleiter, Deformation of Polycrystals: Mechanisms and Microstructures, (edited by N. Hansen, A. Horsewell, T. Leffers and H. Lilholt), p. 15, Riso National Laboratory, Roskilde, Denmark (1981). R.W. Siegel, S. Ramasamy, H. Hahn, L. Zongquan, L. Ting and R. Gronsky, J. Mater. Res. 3, 1367 (1988). E. Hellstern, H.J. Fecht, Z. Fu and W.L. Johnson, J. App. Phys. 65305 (1989). J.S.C. Jang and C.C. Koch, Scripta Metall. Mater. 24, 1599 (1990). D.A. Rigney, Ann. Rev. Mater. Sci. 18, 141 (1988). M. Ciftcioglu and M.J. Mayo, Superplasticity in Metals, Ceramics and Intermetallics, MRS Symposium Proc., vol. 196 (edited by M.J. Mayo, M. Kobayashi and J. Wadsworth), p. 77 (1990). L.E. McCandlish, B.K. Kim and B.H. Kear, High Performance Composites for the 1990's (edited by S.K. Das, C.P. Ballard and F. Marikar), p. 227, TMS, Warrendale, PA (1991). O.D. Sherby and J. Wadsworth, Deformation Processing, (edited by G. Krauss), p. 355, ASM, Metals Park, Ohio (1984). J. Horvath, R. Birringer and H. Gleiter, Solid State Comm. 62, 319 (1987). H. Hahn, J. Logas, H.J. Hofler, P. Kurath and R.S. Averbach, in ref. 9, p. 71 (1990). J.A. Eastman, Y.X. Liao, A. Narayansamy and R.W. Siegel, Processing Science of Advanced Ceramics, MRS Symposium Proc., vol, 155, (edited by I.A. Aksay, G.L. McVay and D.R. Ulrich), p. 255, MRS, Pittsburgh, PA (1989). W.D. Kingery, H.K. Bowen and D.R. Uhlmann, Introduction to Ceramics, Wiley, NY (1976). H.J. Hofler and R.S. Averback, Scripta Metall. Mater. 24, 2401 (1990). H.V. Atkinson, Acta Metall. 36, 469 (1988). S.K. Ganapathi, Ph.D. thesis, Ohio State University (1990). S.K. Ganapathi, M. Aindow, H.L. Fraser and D.A. Rigney, MRS Proc. 206 (in press). C.V. Thompson, Ann. Rev. Mater. Sci. 20, 245 (1990). G.W. Nieman, J.R. Weertman and R.W. Siegel, J. Mater. Res. 6, 1012 (1991). G.W. Nieman and J.R. Weertman, Proceedings of Morris Fine Symposium (in press). H. Hahn, J. Logas and R.S. Averback, J. Mater. Res. ~, 609 (1990). M.J. Mayo, MRS Symposium Proc,, vol. 229 (in press). M. Hillert, Acta Metall. 36, 3177 (1965). R.J. Brook, Ceramic Fabrication Processes, (edited by F.F.Y. Wang), p. 331, Academic Press, New York (1976). D.M. Owen and A.H. Chokshi, to be published. D.J. Srolovitz, G.S. Grest and M.P. Anderson, Acta Metall. 33, 2233 (1985). C.V. Thompson, H.J. Frost and F. Spaepan, Acta Metall. 35, 887 (1987). A.D. Rollett, D.J. Srolovitz and M.P. Anderson, Acta Metall. 37, 1227 (1989). C.J. Simpson, K.T. Aust and W.C. Winegard, Metall. trans. ~, 993 (1971). I.M. Ghauri, M.Z. Butt and S.M. Raza, J. Mater. Sci. 25, 4782 (1990). D.B. Butrymowicz, J.R. Manning and M.E. Read, Diffusion Rate Data and Mass Transport Phenomena for Copper Systems, National Bureau of Standards, Washington, D.C. (1977). S. Sehumacher, R. Birringer, R. Strau~ and H. Gleiter, Acta Metall. 37, 2485 (1989). H. Hahn, H. Hofler and R.S. Averback, Defect and Diffusion Forum, 66-69, 549 (1989).
12
Vol.
25, pp. 2 6 9 9 - 2 7 0 4 , 1991 P r i n t e d in the U . S . A .
Pergamon Press plc All rights reserved
THE KINETICS OF GRAIN GROWTH IN NANOCRYSTALLINE COPPER
S.K. Ganapathi +, D.M. Owen* and A.H. Chokshi* +Center for Magnetic Recording Research *Department of Applied Mechanics and Engineering Sciences University of California, San Diego La Jolla, CA 92093 ( R e c e i v e d A u g u s t 26, 1991) (Revised September 24, 1991)
i. Introduction A decrease in grain size from the micrometer to the nanocrystalline range leads to a significant increase in the fraction of atoms residing at grain boundaries. There has been considerable research activity recently in developing and characterizing nanocrystalline materials in bulk form, as noted in recent reviews on the topic [1-3]. Following the pioneering study by Gleiter [4] to form nanocrystalline metals by an inert gas condensation method [4,5], nanocrystalline materials have also been formed by high energy ball milling [6,7], sliding wear [8] and chemical synthesis techniques [9,10]. Experimental results suggest that nanocrystalline materials may exhibit different physical and mechanical properties from conventional polycrystalline materials. One of the interesting applications for nanocrystalline materials is in superplastic forming. It has been noted that the optimum strain rate for superplasticity (iopt) scales inversely with the grain size (d) as follows: ~^_~ ~ d'q where the exponent q has a value between -2 and 3 [ii]. It is necessary to limit grain growth during the consolidation of nanocrystalline powders to form bulk products, in order to fully exploit the potential superplastic and other structural capabilities of these materials. Early studies indicated that nanocrystalline materials have a remarkable resistance to grain growth. Thus, for example, no grain growth was observed in Cu with a grain size of 8 nm after annealing for 60 hours at 393 K [12]. Subsequent studies on nanocrystalline ceramics confirmed these results, and it was shown that there was very little grain growth below a critical temperature [5,13,14]. Eastman e_!ta_!. [14] attributed the stability of nanocrystalline materials to the narrow grain size distributions in these materials. One of the major limitations of these studies on grain growth is that they were conducted on bulk compacted nanocrystalline materials with a significant level of porosity, ranging from i0 to 25%. It is well known that pores may hinder grain growth during sintering [15]. Hofler and Averback [16] demonstrated recently that a decrease in porosity from 25% to 10% in nanocrystalline TiO 2 can lead to a substantial increase in the grain size after annealing. These results suggest that the intrinsic grain growth characteristics of nanocrystalline materials, in the absence of porosity, may be substantially different from those in porous compacts. To date, these results on somewhat porous TiO 2 are the only published data available on determining the kinetics of grain growth in nanocrystalline materials. Normal grain growth in polycrystalline materials is related to a time invariant form of the grain size distribution [17], so that a simple normalization procedure will enable the superimposition of the distributions at two different time intervals. On the other hand, abnormal grain growth leads to a broadening of the grain size distribution by the growth of a few large grains. Siegel et al. [5] noted that an as-compacted (porous) nanocrystalline TiO 2 appeared to exhibit a log-normal grain size distribution. It is not clear whether fully dense nanocrystalline materials exhibit a log-normal distribution and normal grain growth characteristics.
2699 0036-9748/91 $ 3 . 0 0 + .00 Copyright (c) 1 9 9 1 P e r g a m o n P r e s s
plc
2700
NANOCRYSTALLINE
Cu
The kinetics of normal grain growth in polycrystalline represented by an equation of the following form:
Vol.
25,
No.
materials are usually
dN-d~ -Kt
(i)
where d o is the initial grain size, d is the grain size after annealing for a time period of t, and K and N are constants. Various theories for grain growth lead to values of the exponent N from 1 to 4 [17]. The kinetic constant K may be represented as: KzK o exp(-Q/RT)
(2)
where K o is a constant, Q is the activation energy, R is the gas constant and T is the absolute temperature. Experimental studies on grain growth are usually designed to evaluate the values of N and Q, and to determine the mechanism for grain growth by comparing the experimental values with theoretical predictions. The present investigation was undertaken to characterize the grain growth behavior of nanocrystalline materials in the absence of porosity, with the following two specific objectives: (i) to examine whether such materials display normal grain growth, and (ii) to evaluate the grain growth kinetic exponent N and activation energy Q. 2. Experimental Material and Procedures The nanocrystalline material used in the present investigation was obtained by a process of sliding wear [18]. A stainless steel ring was mounted on a shaft and rotated while in contact with an OFHC copper block under a constant load. The debris was typically in the form of thin flakes with an average thickness of -0.5 ~m, and it was found to consist predominantly of Cu with -0.8% Fe and a thin layer of copper oxide on the surface. A transmission electron microscopy (TEM) study revealed that the wear debris was nanocrystalline with grain sizes ranging from 2 to 30 um [19]. In addition, it was also noted that the wear debris exhibited a slight crystallographic texture [18]. For the present experiments, all of the copper debris was initially annealed for 7 minutes at 473 K in hydrogen to reduce the oxide layers on the surfaces. Investigation by bright field TEM revealed the absence of porosity in the wear debris. The wear debris was ideally suited for the present investigation, because the particles were fully dense and it was therefore possible to study grain growth in nanocrystalline copper, in the absence of porosity. For the grain growth study, the debris was encapsulated in quartz tubes which were evacuated and then sealed. Different vials were then annealed at 575, 625 and 675 K for periods of I, 4 and 20 hours. The annealed, powders were mixed with acetone and treated in an ultrasonic bath to break up loose agglomerates and separate the particles. The powder suspension was then sprayed on to a carbon film deposited on a mica substrate, picked up on a 200 mesh copper grid and examined by TEM. The debris particles were thin enough to be electron transparent. The annealed powders were examined at 300 kV in a Philips CM30 TEM. A series of dark field images was obtained from all the annealed specimens by placing the objective aperture over a section of the (Iii) diffraction rings. The grain size distributions were characterized from these micrographs using a video image analysis system connected to a personal computer. A sufficient number of measurements were recorded to minimize errors in determining the grain size. 3, Experimental Results The transmission electron microscopy investigation revealed that the individual particle sizes were similar before and after annealing, thereby indicating the absence of significant sintering and agglomeration. Measurements indicated that the average initial grain size was 18±1.1 nm, prior to annealing the specimens for the grain growth study. The largest linear dimensions of the crystallites were recorded from the micrographs, and some of the typical experimental results are shown in Fig. i in the form of histograms
12
Vol.
25, No.
12
NANOCRYSTALLINE
Cu
2701
depicting the size distribution of crystallites after i and 20 hours of annealing at 625 K. The histograms suggest that the grain sizes follow a log-normal distribution. All of the experimental results obtained in the present investigation are summarized in Fig. 2, which shows the variation in average grain size with annealing time at three different temperatures. The error bars on the datum points tend to be in the range of ~I0% error at the 95% confidence limit. The results shown in Fig. 2 indicate that the largest average grain size achieved in the present study was -55 nm after annealing for 20 hours at 675 K.
40
2O Cu
Nanocrystalline
>
T = 625 K t = 3.6x103
30
d =
>,
T = 625 K t = 7.2x104
15
s
22.6±1.1
Cu
Nanocrystalline
nm
o"
~ 2c
lO
u.
U.
s
5 @
n" m
25
0
75
50 cl i
100
125
150
0
25
75
50 di
(nrn)
(a)
100
125
150
(nm)
(b)
Fig. I Histograms showing size distribution of nanocrystalline Cu grains after annealing at 625 K for (a) I hour and (b) 20 hours.
70
I
I
I
I
I
I
I
I
I
Nanocrystalline Cu [] initial
T~
T (K) 50
A 625
E v
/
~
c
-0
30
10
I
0
Fig. 2
I
I
20
I
I
I
40 3 10 t (s)
I
I
60
Variation in average grain size with annealing time and temperature.
I
80
2702
NANOCRYSTALLINE
Cu
Vol.
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4. Discussion 4,1 The Validity of the Present Experimental Results It is necessary to evaluate the possibility that the present experimental results were influenced by the small sizes of the debris particles (-0.5 ~m). As noted by Thompson [20] in a review of grain growth in thin films, grain growth in an equiaxed structure in thin films occurs in a manner similar to that in bulk polycrystalline materials until the grains grow to dimensions equal to the film thickness. Even at the coarsest grain sizes encountered in this study, there were likely to be more than -4 to 5 grains across the thickness of the particles. Consequently, the present results are not likely to have been influenced by the fine sizes of the debris. The grain sizes in nanoerystalline materials have been estimated from x-ray diffraction peak broadening techniques [6,7,21,22] or determined directly by TEM [5,12,23]. Nieman and Weertman [22] conducted a detailed investigation to determine grain sizes by x-ray diffraction, and they concluded that the errors in the measurements are of the order of K25% and KI00% for grain sizes of K25 nm and k50 nm, respectively. In view of these relatively large errors, the direct measurements recorded in the present investigation are preferable due to the smaller errors of s10%. In addition, the large strains associated with the wear debris are likely to increase the errors in grain size determination by x-ray diffraction. The nanocrystalline materials generally produce a ring diffraction pattern in TEM studies. A portion of the ring is utilized in producing the dark field images used for grain size measurements. With the smallest aperture available, simple calculations indicate that the present technique is not capable of distinguishing between adjacent grains if their misorientations are ~5 ° . However, since grain growth proceeds largely by the migration of high angle grain boundaries, the above difficulty is not a serious limitation. Finally, it is important to note that nanocrystalline materials produced by different techniques may lead to variations in mechanical characteristics. Thus, for example, Mayo [24] has demonstrated recently that nanocrystalline Cu produced by the inert gas atomization technique and by the sliding wear process exhibit substantially different hardness characteristics, in spite of their nominally similar grain sizes. 4.2 The Characteristics of Grain Growth Normal grain growth is characterized by a time invariant shape of size distribution; normalizing the distributions by the respective average grain sizes will lead to the superimposition of the distributions at different time i
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dild Fig. 3 Cumulative probability vs normalized grain size for the nanocrystalline Cu annealed at 625 K for i, 4 and 20 hours: size distributions are normalized by average grain sizes.
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intervals. The present experimental results were tested for this behavior by plotting the results in the form shown in Fig. 3: on such a plot, a log-normal distribution will lead to the data falling on a straight line. Inspection of the experimental results shown for grain growth at 625 K indicate that the data for three different annealing times fall essentially on a single straight line, thereby confirming the occurrence of normal grain growth in the nanocrystalline material with a log-normal distribution. Similar results were obtained at the two other temperatures used in this investigation. Hillert [25] has examined theoretically the conditions necessary for the onset of abnormal grain growth, and concluded that abnormal grain growth is likely when the ratio of largest grain size to average grain size, dmax/d, in a material is >2. Brook [26] noted qualitatively that a ratio of dmax/d >2.5 to 3 is necessary for abnormal grain growth. The experimental results in the present study indicate that normal grain growth occurs in spite of the ratio dmax/d being ~3. A similar result was noted in an earlier study on static grain growth in a ZRO2-20% AI203 composite [27]. These experimental observations are consistent with the computer simulations of Srolovitz et al. [28] which indicate that the presence of grains significantly larger than the average value does not necessarily lead to abnormal growth. Thompson e__tta l. [29] obtained a similar result analytically, and this was extended by Rollett et al. [30] to include anisotropies in grain boundary mobilities. 4.3 The Kinetics of Grain Growth The correlation coefficients, r, were evaluated for values of N equal to 2, 3 and 4 in eqn. I, to determine the appropriate grain growth exponent. The experimental results for the three different temperatures indicated that there was very little difference in r for the different exponents. Thus, calculations at 625 K indicated that the values of r are 0.96, 0.99 and 1.0 for N=2, 3 and 4, respectively. A similar evaluation of the exponent N, using the data reported for porous nanocrystalline TiO 2 by Hofler and Averbach [16], indicated that the values of r are -0.98, 0.98 and 0.97 for N-2, 3 and 4, respectively. Very similar results were obtained in an earlier study on static grain growth of fully dense microduplex ZRO2-20% AI203 composite [27]. The relatively minor differences in the correlation coefficients obtained are not necessarily related to the small statistical sample size. Thus, for example, a re-evaluation of data on grain growth in high purity Cd [31] with 17 datum points indicated that the values of r are 0.98, 0.98 and 0.95 for N-2, 3 and 4, respectively: the data had been analyzed originally only in terms of N~2 [31]. The present analysis indicates that it is difficult to identify a grain growth mechanism on the basis of the exponent N. Also, as noted by Atkinson [17], several different mechanisms may be contributing to commonly reported exponents such as N=3. The activation energy for grain growth may be calculated using eqns. i and 2 with an appropriate value of N. Using N=4 for the present experimental results, the activation energy for grain growth was calculated to be 30±9 kJ mol -I. This value is much smaller than that reported (-80 kJ mol -I) for grain growth in polyerystalline Cu [32]. An activation energy of -i00 kJ mol "I (-0.5 Q~, where Q~ is the activation energy for lattice diffusion) is usually accepted as the value for grain boundary diffusion in polycrystalline copper, and the present activation energy is much smaller than the values reported in coarser grained polycrystalline Cu [33]. The large stored energy of cold work associated with sliding wear may have contributed to the low activation energy obtained in this investigation. Horvath e t a l. [12] and Schumacher et al. [34] determined the coefficients for diffusion in nanocrystalline Cu, with a relative density of -90%, for Cu and Ag, respectively: activation energies in the range of 38 to 66 kJ mol "I were reported. It is important to note that the diffusion data in nanocrystalline copper were obtained at a lower temperature range of 293 to 393 K in comparison with the temperature range of 575 to 675 K used in the present investigation. Additionally, it has been suggested that the lower activation energies obtained in nanocrystalline Cu [12,34] were a consequence of the porous nature of the specimens used in those investigations [35]. 5.
Summary and Conclusions
Grain growth in nanocrystalline copper was studied in the absence of porosity using wear debris obtained from sliding wear experiments. The results demonstrate for the first
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time that grain growth in nanocrystalline materials occurs in a normal manner, so that the log-normal form of the grain size distribution curve is not altered during grain growth. The analysis indicates that it is generally difficult to evaluate a grain growth exponent N, because very similar correlation coefficients are obtained with N values of 2, 3 and 4. The analysis also yielded a rather low value of activation energy for grain growth. Acknowledgement This work was supported in part by ARO under contract no. DAAL86-K-0169 and the National Science Foundation under Grant no. DMR-9023699. The authors are grateful to Dr. D.A. Rigney of Ohio State University for assistance in obtaining the Cu powders. References i. 2. 3. 4.
5. 6. 7. 8. 9.
i0. ii. 12. 13. 14.
15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.
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