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The effects of triple junctions and grain boundaries on hardness and Young’s modulus in nanostructured Ni–P
Scripta Materialia 48 (2003) 825–830 www.actamat-journals.com
The effects of triple junctions and grain boundaries on hardness and YoungÕs modulus in nanostructured Ni–P Y. Zhou a, U. Erb a
a,*
, K.T. Aust a, G. Palumbo
b
Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, Ont., Canada M5S 3E4 b Integran Technologies Inc., 1 Meridian Road, Toronto, Ont., Canada M9W 4Z6 Received 4 July 2002; received in revised form 16 October 2002; accepted 17 October 2002
Abstract Hardness and YoungÕs modulus were measured on a series of nanocrystalline Ni–P samples. With decreasing grain size, a transition from regular to inverse Hall–Petch relationship and a reduction in YoungÕs modulus at the smallest grain sizes was observed, which can be attributed to grain boundary and triple junction effect. Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Interfaces; Mechanical properties; Nanoindentation; Nanocrystalline materials; Electroplating
1. Introduction Owing to the fact that a considerable fraction of atoms reside in interfacial regions, nanocrystalline materials often exhibit quite different properties than their conventional polycrystalline counterpart. While for some properties it may be quite sufficient to consider only the total volume fraction of the material associated with the interfaces, other phenomena require a detailed analysis of the various contributing factors such as grain boundaries (GB), triple junctions (TJ) and quadruple nodes [1,2], in particular for grain sizes less than 30 nm. Palumbo et al. [1] first recognized that the triple junction volume fraction actually shows a greater grain size dependence than the grain
* Corresponding author. Tel.: +1-4169784430; fax: +14169463316. E-mail address: [email protected] (U. Erb).
boundary volume fraction at grain sizes below 30 nm. Using a regular 14 sided tetrakaidecahedron as a grain shape, the volume fraction of atoms associated with grain boundaries and triple junctions as a function of grain size and grain boundary thickness was computed as described in detail in [1]. The results of such computations for a grain boundary thickness of 1 nm are plotted in Fig. 1 for grain sizes smaller than 40 nm. As can be seen from Fig. 1, for grain sizes larger than 30 nm the contribution of the triple junction volume fraction to the total interface volume fraction is negligible. In other words, for large grain sizes, the intercrystalline volume fraction is made up almost entirely of grain boundary atoms. However, for grain sizes less than 30 nm, the volume fraction of the triple junctions increases more rapidly with decreasing grain size than the grain boundary volume fraction, because of the stronger grain size dependence. The consequence of this is that the relative contribution of the triple junction volume
1359-6462/03/$ - see front matter Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 2 ) 0 0 5 1 1 - 0
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Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
Fig. 1. Volume fractions of GB, TJ and interface as a function of grain size.
fraction to the total interface component becomes comparable to the grain boundary contribution for very small grain sizes. Surprisingly, for the smallest grain sizes (<3 nm), the triple junction contribution actually dominates over the grain boundary contribution. Since triple junctions in polycrystalline materials have long been known to be distinct microstructural defects in polycrystalline materials [3] with unique physical [4,5] and chemical [6,7] properties, it is reasonable to expect changes in some properties of nanocrystalline materials when the grain size is in the range in which the triple junction volume fraction becomes significant (<30 nm). In fact, in previous studies, a number of observations on nanocrystalline materials have already been interpreted in terms of triple junction effects. These include the transition from regular to inverse Hall– Petch behavior in nanocrystalline Ni–P alloys [6], the enhanced hydrogen permeation in nanocrystalline Ni [8] and the thermal stability of nanocrystalline Ni (triple junction drag) [9]. One particular property which may also show distinctive triple junction phenomena is the YoungÕs modulus. In the past, studies on the effect of crystal size reduction on YoungÕs modulus have produced conflicting results. Initially, very large reductions in YoungÕs modulus have been observed in nanocrystalline materials produced by compaction of precursor powders e.g. [10]. On the other hand, fully dense nanocrystalline materials
produced by electrodeposition showed little grain size dependence of YoungÕs modulus, at least for materials with grain size larger than 7 nm [11]. It was speculated that the large reduction in YoungÕs modulus observed in compacted materials was due to residual porosity [10]. Krstic et al. [12] and Zugic et al. [13] showed that large reductions in YoungÕs modulus in nanocrystalline metals containing residual porosity can actually be predicted by applying a porosity model, previously developed for other strong solids, which considers the crack opening displacement of annular flaws associated with pores as the main contributing factor in the reduction of the YoungÕs modulus. Subsequent measurements (e.g. [14]) on compacted nanocrystalline metals with lower residual porosity confirmed that the initially reported large reductions in YoungÕs modulus were indeed mainly the result of residual porosity. What remains to be investigated is the effect of the two main intercrystalline volume fraction contributions at very small grain sizes on YoungÕs modulus. Since most of the previous work dealt with grain sizes larger than 10 nm at which the triple junction volume fraction is still less than 5% (Fig. 1), triple junction effects may not have been significant. The purpose of our current study is to examine the change in YoungÕs modulus as a function of grain size for materials with grain sizes ranging from about 30 nm down to less than 5 nm, covering a wide range of triple junction volume fractions.
2. Experimental Electrodeposition was the technique used in synthesizing the Ni–P alloy samples with negligible porosity. The plating bath contained nickel sulphate, nickel chloride, phosphoric and phosphorous acid. Details of synthesis parameters and bath chemistry can be found elsewhere [15,16]. By adjusting plating parameters, nanocrystalline Ni–P alloys were plated to a thickness of 100–150 lm onto a Ti substrate, having fully dense structure and constant P content (2.0 wt.% as per energy dispersive X-ray spectroscopy). Average grain sizes were determined from transmission electron
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
microscopy (TEM) dark field images by counting at least 160 grain diameters. The hardness and elastic modulus were determined on a SHIMADZU Dynamic Ultra-micro Hardness Tester with Berkovich nanoindenter. Prior to measurements, the samples were mechanically ground and polished, using alumina with particle sizes down to 0.05 lm. Cyclic loading was the loading mode used for the measurements with four cycles for a given load so that the last unloading curve was almost pure elastic, allowing a reliable elastic modulus determination [17]. Each sample was measured under five different loads (150, 130, 110, 90 and 70 mN) with two trials for each load. The loading rate was 13.3 mN/s for all loads. The elastic unloading curves were analyzed to determine hardness and YoungÕs modulus, using the procedure proposed by Oliver and Pharr [17].
3. Results and discussion Table 1 summarizes the average grain size, phosphorus P content, and the volume fractions of interfacial components of four different samples used in the current study. Note that the grain sizes of the samples used in this study are shown by the dashed lines in Fig. 1. Figs. 2 and 3 show representative TEM dark field images, electron diffraction patterns and X-ray diffraction (XRD) patterns, respectively, of Samples 1 and 3. Fig. 4 shows the hardness measurements both in VHN and GPa units in the form of a Hall–Petch plot. A conventional Hall–Petch relationship, i.e. increasing hardness with decreasing grain size, is observed for the larger grain sizes. However the
smallest grain size shows a considerable reduction in hardness. This observed transition from regular to inverse Hall–Petch relationship is quite similar to the one observed by Palumbo et al. [18] also for electrodeposited nanocrystalline Ni–P samples, which they attributed to the triple junction softening effect. Although phosphorus may have some influence on the observed hardness behavior, its overall effect is likely minor in comparison with grain size effect, as similar transitions from regular to inverse Hall–Petch behavior were also observed for pure Ni and Ni–Fe electrodeposits without any phosphorus addition [19]. Fig. 5 shows the YoungÕs modulus as a function of grain size. Initially, the YoungÕs modulus shows a continuous decrease from 205 GPa at a grain size of about 30 nm (which is close to the value of 207 GPa for conventional polycrystalline Ni [20]) to 188 GPa at a grain size of 7 nm, followed by a relatively sharp drop for the smallest grain size. It is quite interesting to note that the initial decrease in YoungÕs modulus correlates well with the increase in the total interface volume fraction, i.e. triple junctions and grain boundaries together (Fig. 6). This suggests that both grain boundaries and triple junctions have a contribution to the decrease in the YoungÕs modulus. However, the steep increase in the triple junction volume fraction largely accounts for the sharp drop in the YoungÕs modulus at the smallest grain size (4 nm). If the nanocrystalline material is considered a composite consisting of grain matrix, grain boundaries and triple junctions, the relative contributions of the three components to the YoungÕs modulus could be assessed by using a simple rule of mixture for composite materials of the following form [21]: Em ¼ EG fG þ EGB fGB þ ETJ fTJ
Table 1 Average grain size, P content and volume fractions of GB, TJ and total interface for Samples 1-4 Sample no. d (nm) P (wt.%) Volume fractions
Interface GB TJ
1
2
3
4
4.1 2.0 0.623 0.369 0.254
7.1 2.0 0.408 0.313 0.0948
17.1 2.1 0.187 0.169 0.0178
28.9 2.1 0.114 0.107 0.00636
827
ð1Þ
where Em is the measured YoungÕs modulus of the material, fG (EG ), fGB (EGB ) and fTJ (ETJ ) the volume fractions (average YoungÕs moduli) for grain matrix, grain boundaries and triple junctions, respectively. Using the measured Em values, the calculation shows that EG ¼ 204 GPa, EGB ¼ 184 GPa and ETJ ¼ 143 GPa. The reduced YoungÕs modulus at the grain boundaries and triple junctions can be attributed
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Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
Fig. 2. TEM images of Sample 1 with a grain size of 4.1 nm, (a) dark field, and (b) diffraction pattern, and Sample 3 with a grain size of 17.1 nm, (c) dark field, and (d) diffraction pattern.
to the increased free volume in the interfacial region. For example, by measuring the positron lifetime in nanocrystalline Fe, Schaefer et al. [22] found that the free volume at grain boundaries is larger than in the perfect crystal lattice. This means that the average interatomic spacing in the grain boundaries is increased compared to that in the perfect crystal lattice. Even larger free volumes were observed at triple junctions [22]. Assuming the same interatomic potential in the interfacial region as in the perfect crystal lattice, the increase in interatomic spacing would result in a reduction
in YoungÕs modulus. Therefore, the relative large YoungÕs modulus reduction at triple junctions (ETJ ¼ 143 GPa) is likely the direct result of their larger average interatomic spacings, compared with grain boundaries.
4. Conclusions Nanoindentaion measurements on a series of nanocrystalline Ni–P samples having fully dense structure and constant P content show a transition
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
Fig. 3. XRD patterns of Samples 1 and 3.
829
Fig. 6. Comparison between the YoungÕs modulus and the interfacial volume fractions.
from regular to inverse Hall–Petch relationship with decreasing grain size, which can be explained in terms of triple junction contributions. A continuous decrease in YoungÕs modulus at grain sizes below 30 nm was observed, which is considered to be the result of all interface contributions. The large drop in YoungÕs modulus at a grain size of 4.1 nm is mainly due to the sharp increase of triple junction volume fraction. Using a simple composite model, the YoungÕs moduli of the grain boundary and triple junction components were determined to be 184 and 143 GPa, respectively.
Fig. 4. Hardness as a function of grain size in nanocrystalline Ni–P.
Acknowledgements The authors would like to thank Shimadzu Corporation for their generous donation of the nanoindenter, and Dr. G. Hibbard from Integran Technology Inc. for his contributions. Financial support from the Natural Sciences and Engineering Research Council of Canada and the Ontario Graduate Scholarship is gratefully acknowledged.
References
Fig. 5. Elastic modulus as a function of grain size in nanocrystalline Ni–P.
[1] Palumbo G, Thorpe SJ, Aust KT. Scripta Metall Mater 1990;24:1347. [2] Chokshi AH, Rosen A, Karch J, Gleiter H. Scripta Metall Mater 1989;23:1679. [3] Bollmann W. Phil Mag A 1984;49(1):73, 1988;57(4):637 Mater Sci Eng A 1988;113:129. [4] Rabukhin VB. Phys Met Metalloved 1986;61:149.
830
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
[5] Lehockey EM, Palumbo G, Erb U, Aust KT, Lin P. Scripta Mater 1998;39(3):341. [6] Palumbo G, Aust KT. Mater Sci Eng A 1989;113:139. [7] Zhou Y, Erb U, Aust KT, Palumbo G. ASM International, Processing and fabrication of advanced materials X (USA); 2002. p. 438. [8] Palumbo G, Doyle DM, El-Sherik AM, Erb U, Aust KT. Scripta Metall Mater 1991;25:679. [9] Boylan K, Ostrander D, Erb U, Palumbo G, Aust KT. Scripta Metall Mater 1991;25(12):2711. [10] Nieman GW, Weertman JR, Siegel RW. J Mater Res 1991;6:1012. [11] Wong L, Ostrander D, Erb U, Palumbo G, Aust KT. In: Shull RD, Sanchez JM, editors. Nanophase and nanocrystalline structures. Warrendale, Pennsylvania: Metallurgical Society of AIME; 1994. p. 85. [12] Krstic VD, Erb U, Palumbo G. Scripta Metall Mater 1993;29:1501.
[13] Zugic R, Szpunar B, Krstic VD, Erb U. Phil Mag A 1997;75(4):1041. [14] Sanders PG, Youngdahl CG, Weertman JR. Mater Sci Eng A 1997;234–236:77. [15] Erb U, El-Sherik AM. US Patent No. 5 353 266 (1994). [16] McMahon G, Erb U. Microstr Sci 1989;17:447. [17] Oliver WC, Pharr GM. J Mater Res 1992;7(6):1564. [18] Palumbo G, Erb U, Aust KT. Scripta Metall Mater 1990;24:2347. [19] Erb U, Palumbo G, Zugic R, Aust KT. In: Suryanarayana C et al., editors. Processing and properties of nanocrystalline materials. Warredale, Pennsylvania: TMS; 1996. p. 93. [20] Weast RC, editor in chief. CRC handbook of chemistry and physics, 1st student ed. Florida: CRC Press Inc.; 1988. [21] Paul B. Trans AIME 1960;218:36. [22] Schaefer HE, Wurschum R, Birringer R, Gleiter H. Phys Rev B 1988;38:9545.
The effects of triple junctions and grain boundaries on hardness and YoungÕs modulus in nanostructured Ni–P Y. Zhou a, U. Erb a
a,*
, K.T. Aust a, G. Palumbo
b
Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, Ont., Canada M5S 3E4 b Integran Technologies Inc., 1 Meridian Road, Toronto, Ont., Canada M9W 4Z6 Received 4 July 2002; received in revised form 16 October 2002; accepted 17 October 2002
Abstract Hardness and YoungÕs modulus were measured on a series of nanocrystalline Ni–P samples. With decreasing grain size, a transition from regular to inverse Hall–Petch relationship and a reduction in YoungÕs modulus at the smallest grain sizes was observed, which can be attributed to grain boundary and triple junction effect. Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Interfaces; Mechanical properties; Nanoindentation; Nanocrystalline materials; Electroplating
1. Introduction Owing to the fact that a considerable fraction of atoms reside in interfacial regions, nanocrystalline materials often exhibit quite different properties than their conventional polycrystalline counterpart. While for some properties it may be quite sufficient to consider only the total volume fraction of the material associated with the interfaces, other phenomena require a detailed analysis of the various contributing factors such as grain boundaries (GB), triple junctions (TJ) and quadruple nodes [1,2], in particular for grain sizes less than 30 nm. Palumbo et al. [1] first recognized that the triple junction volume fraction actually shows a greater grain size dependence than the grain
* Corresponding author. Tel.: +1-4169784430; fax: +14169463316. E-mail address: [email protected] (U. Erb).
boundary volume fraction at grain sizes below 30 nm. Using a regular 14 sided tetrakaidecahedron as a grain shape, the volume fraction of atoms associated with grain boundaries and triple junctions as a function of grain size and grain boundary thickness was computed as described in detail in [1]. The results of such computations for a grain boundary thickness of 1 nm are plotted in Fig. 1 for grain sizes smaller than 40 nm. As can be seen from Fig. 1, for grain sizes larger than 30 nm the contribution of the triple junction volume fraction to the total interface volume fraction is negligible. In other words, for large grain sizes, the intercrystalline volume fraction is made up almost entirely of grain boundary atoms. However, for grain sizes less than 30 nm, the volume fraction of the triple junctions increases more rapidly with decreasing grain size than the grain boundary volume fraction, because of the stronger grain size dependence. The consequence of this is that the relative contribution of the triple junction volume
1359-6462/03/$ - see front matter Ó 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 6 2 ( 0 2 ) 0 0 5 1 1 - 0
826
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
Fig. 1. Volume fractions of GB, TJ and interface as a function of grain size.
fraction to the total interface component becomes comparable to the grain boundary contribution for very small grain sizes. Surprisingly, for the smallest grain sizes (<3 nm), the triple junction contribution actually dominates over the grain boundary contribution. Since triple junctions in polycrystalline materials have long been known to be distinct microstructural defects in polycrystalline materials [3] with unique physical [4,5] and chemical [6,7] properties, it is reasonable to expect changes in some properties of nanocrystalline materials when the grain size is in the range in which the triple junction volume fraction becomes significant (<30 nm). In fact, in previous studies, a number of observations on nanocrystalline materials have already been interpreted in terms of triple junction effects. These include the transition from regular to inverse Hall– Petch behavior in nanocrystalline Ni–P alloys [6], the enhanced hydrogen permeation in nanocrystalline Ni [8] and the thermal stability of nanocrystalline Ni (triple junction drag) [9]. One particular property which may also show distinctive triple junction phenomena is the YoungÕs modulus. In the past, studies on the effect of crystal size reduction on YoungÕs modulus have produced conflicting results. Initially, very large reductions in YoungÕs modulus have been observed in nanocrystalline materials produced by compaction of precursor powders e.g. [10]. On the other hand, fully dense nanocrystalline materials
produced by electrodeposition showed little grain size dependence of YoungÕs modulus, at least for materials with grain size larger than 7 nm [11]. It was speculated that the large reduction in YoungÕs modulus observed in compacted materials was due to residual porosity [10]. Krstic et al. [12] and Zugic et al. [13] showed that large reductions in YoungÕs modulus in nanocrystalline metals containing residual porosity can actually be predicted by applying a porosity model, previously developed for other strong solids, which considers the crack opening displacement of annular flaws associated with pores as the main contributing factor in the reduction of the YoungÕs modulus. Subsequent measurements (e.g. [14]) on compacted nanocrystalline metals with lower residual porosity confirmed that the initially reported large reductions in YoungÕs modulus were indeed mainly the result of residual porosity. What remains to be investigated is the effect of the two main intercrystalline volume fraction contributions at very small grain sizes on YoungÕs modulus. Since most of the previous work dealt with grain sizes larger than 10 nm at which the triple junction volume fraction is still less than 5% (Fig. 1), triple junction effects may not have been significant. The purpose of our current study is to examine the change in YoungÕs modulus as a function of grain size for materials with grain sizes ranging from about 30 nm down to less than 5 nm, covering a wide range of triple junction volume fractions.
2. Experimental Electrodeposition was the technique used in synthesizing the Ni–P alloy samples with negligible porosity. The plating bath contained nickel sulphate, nickel chloride, phosphoric and phosphorous acid. Details of synthesis parameters and bath chemistry can be found elsewhere [15,16]. By adjusting plating parameters, nanocrystalline Ni–P alloys were plated to a thickness of 100–150 lm onto a Ti substrate, having fully dense structure and constant P content (2.0 wt.% as per energy dispersive X-ray spectroscopy). Average grain sizes were determined from transmission electron
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
microscopy (TEM) dark field images by counting at least 160 grain diameters. The hardness and elastic modulus were determined on a SHIMADZU Dynamic Ultra-micro Hardness Tester with Berkovich nanoindenter. Prior to measurements, the samples were mechanically ground and polished, using alumina with particle sizes down to 0.05 lm. Cyclic loading was the loading mode used for the measurements with four cycles for a given load so that the last unloading curve was almost pure elastic, allowing a reliable elastic modulus determination [17]. Each sample was measured under five different loads (150, 130, 110, 90 and 70 mN) with two trials for each load. The loading rate was 13.3 mN/s for all loads. The elastic unloading curves were analyzed to determine hardness and YoungÕs modulus, using the procedure proposed by Oliver and Pharr [17].
3. Results and discussion Table 1 summarizes the average grain size, phosphorus P content, and the volume fractions of interfacial components of four different samples used in the current study. Note that the grain sizes of the samples used in this study are shown by the dashed lines in Fig. 1. Figs. 2 and 3 show representative TEM dark field images, electron diffraction patterns and X-ray diffraction (XRD) patterns, respectively, of Samples 1 and 3. Fig. 4 shows the hardness measurements both in VHN and GPa units in the form of a Hall–Petch plot. A conventional Hall–Petch relationship, i.e. increasing hardness with decreasing grain size, is observed for the larger grain sizes. However the
smallest grain size shows a considerable reduction in hardness. This observed transition from regular to inverse Hall–Petch relationship is quite similar to the one observed by Palumbo et al. [18] also for electrodeposited nanocrystalline Ni–P samples, which they attributed to the triple junction softening effect. Although phosphorus may have some influence on the observed hardness behavior, its overall effect is likely minor in comparison with grain size effect, as similar transitions from regular to inverse Hall–Petch behavior were also observed for pure Ni and Ni–Fe electrodeposits without any phosphorus addition [19]. Fig. 5 shows the YoungÕs modulus as a function of grain size. Initially, the YoungÕs modulus shows a continuous decrease from 205 GPa at a grain size of about 30 nm (which is close to the value of 207 GPa for conventional polycrystalline Ni [20]) to 188 GPa at a grain size of 7 nm, followed by a relatively sharp drop for the smallest grain size. It is quite interesting to note that the initial decrease in YoungÕs modulus correlates well with the increase in the total interface volume fraction, i.e. triple junctions and grain boundaries together (Fig. 6). This suggests that both grain boundaries and triple junctions have a contribution to the decrease in the YoungÕs modulus. However, the steep increase in the triple junction volume fraction largely accounts for the sharp drop in the YoungÕs modulus at the smallest grain size (4 nm). If the nanocrystalline material is considered a composite consisting of grain matrix, grain boundaries and triple junctions, the relative contributions of the three components to the YoungÕs modulus could be assessed by using a simple rule of mixture for composite materials of the following form [21]: Em ¼ EG fG þ EGB fGB þ ETJ fTJ
Table 1 Average grain size, P content and volume fractions of GB, TJ and total interface for Samples 1-4 Sample no. d (nm) P (wt.%) Volume fractions
Interface GB TJ
1
2
3
4
4.1 2.0 0.623 0.369 0.254
7.1 2.0 0.408 0.313 0.0948
17.1 2.1 0.187 0.169 0.0178
28.9 2.1 0.114 0.107 0.00636
827
ð1Þ
where Em is the measured YoungÕs modulus of the material, fG (EG ), fGB (EGB ) and fTJ (ETJ ) the volume fractions (average YoungÕs moduli) for grain matrix, grain boundaries and triple junctions, respectively. Using the measured Em values, the calculation shows that EG ¼ 204 GPa, EGB ¼ 184 GPa and ETJ ¼ 143 GPa. The reduced YoungÕs modulus at the grain boundaries and triple junctions can be attributed
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Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
Fig. 2. TEM images of Sample 1 with a grain size of 4.1 nm, (a) dark field, and (b) diffraction pattern, and Sample 3 with a grain size of 17.1 nm, (c) dark field, and (d) diffraction pattern.
to the increased free volume in the interfacial region. For example, by measuring the positron lifetime in nanocrystalline Fe, Schaefer et al. [22] found that the free volume at grain boundaries is larger than in the perfect crystal lattice. This means that the average interatomic spacing in the grain boundaries is increased compared to that in the perfect crystal lattice. Even larger free volumes were observed at triple junctions [22]. Assuming the same interatomic potential in the interfacial region as in the perfect crystal lattice, the increase in interatomic spacing would result in a reduction
in YoungÕs modulus. Therefore, the relative large YoungÕs modulus reduction at triple junctions (ETJ ¼ 143 GPa) is likely the direct result of their larger average interatomic spacings, compared with grain boundaries.
4. Conclusions Nanoindentaion measurements on a series of nanocrystalline Ni–P samples having fully dense structure and constant P content show a transition
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
Fig. 3. XRD patterns of Samples 1 and 3.
829
Fig. 6. Comparison between the YoungÕs modulus and the interfacial volume fractions.
from regular to inverse Hall–Petch relationship with decreasing grain size, which can be explained in terms of triple junction contributions. A continuous decrease in YoungÕs modulus at grain sizes below 30 nm was observed, which is considered to be the result of all interface contributions. The large drop in YoungÕs modulus at a grain size of 4.1 nm is mainly due to the sharp increase of triple junction volume fraction. Using a simple composite model, the YoungÕs moduli of the grain boundary and triple junction components were determined to be 184 and 143 GPa, respectively.
Fig. 4. Hardness as a function of grain size in nanocrystalline Ni–P.
Acknowledgements The authors would like to thank Shimadzu Corporation for their generous donation of the nanoindenter, and Dr. G. Hibbard from Integran Technology Inc. for his contributions. Financial support from the Natural Sciences and Engineering Research Council of Canada and the Ontario Graduate Scholarship is gratefully acknowledged.
References
Fig. 5. Elastic modulus as a function of grain size in nanocrystalline Ni–P.
[1] Palumbo G, Thorpe SJ, Aust KT. Scripta Metall Mater 1990;24:1347. [2] Chokshi AH, Rosen A, Karch J, Gleiter H. Scripta Metall Mater 1989;23:1679. [3] Bollmann W. Phil Mag A 1984;49(1):73, 1988;57(4):637 Mater Sci Eng A 1988;113:129. [4] Rabukhin VB. Phys Met Metalloved 1986;61:149.
830
Y. Zhou et al. / Scripta Materialia 48 (2003) 825–830
[5] Lehockey EM, Palumbo G, Erb U, Aust KT, Lin P. Scripta Mater 1998;39(3):341. [6] Palumbo G, Aust KT. Mater Sci Eng A 1989;113:139. [7] Zhou Y, Erb U, Aust KT, Palumbo G. ASM International, Processing and fabrication of advanced materials X (USA); 2002. p. 438. [8] Palumbo G, Doyle DM, El-Sherik AM, Erb U, Aust KT. Scripta Metall Mater 1991;25:679. [9] Boylan K, Ostrander D, Erb U, Palumbo G, Aust KT. Scripta Metall Mater 1991;25(12):2711. [10] Nieman GW, Weertman JR, Siegel RW. J Mater Res 1991;6:1012. [11] Wong L, Ostrander D, Erb U, Palumbo G, Aust KT. In: Shull RD, Sanchez JM, editors. Nanophase and nanocrystalline structures. Warrendale, Pennsylvania: Metallurgical Society of AIME; 1994. p. 85. [12] Krstic VD, Erb U, Palumbo G. Scripta Metall Mater 1993;29:1501.
[13] Zugic R, Szpunar B, Krstic VD, Erb U. Phil Mag A 1997;75(4):1041. [14] Sanders PG, Youngdahl CG, Weertman JR. Mater Sci Eng A 1997;234–236:77. [15] Erb U, El-Sherik AM. US Patent No. 5 353 266 (1994). [16] McMahon G, Erb U. Microstr Sci 1989;17:447. [17] Oliver WC, Pharr GM. J Mater Res 1992;7(6):1564. [18] Palumbo G, Erb U, Aust KT. Scripta Metall Mater 1990;24:2347. [19] Erb U, Palumbo G, Zugic R, Aust KT. In: Suryanarayana C et al., editors. Processing and properties of nanocrystalline materials. Warredale, Pennsylvania: TMS; 1996. p. 93. [20] Weast RC, editor in chief. CRC handbook of chemistry and physics, 1st student ed. Florida: CRC Press Inc.; 1988. [21] Paul B. Trans AIME 1960;218:36. [22] Schaefer HE, Wurschum R, Birringer R, Gleiter H. Phys Rev B 1988;38:9545.