- Email: [email protected]
Size effects in properties of nanomaterials
Scripta mater. 44 (2001) 1621–1624 www.elsevier.com/locate/scriptamat
SIZE EFFECTS IN PROPERTIES OF NANOMATERIALS R.A. Andrievski1 and A.M. Glezer2 1
Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, 142432 Russia 2Institute of Physical Metallurgy and Functional Materials, State Scientific Center, “I.P. Bardin Central Research Institute for the Iron/Steel Industry,” Moscow, 107005, Russia (Received August 21, 2000) (Accepted in revised form December 27, 2000)
Keywords: Nanostructured materials; Size effect; Structure-property relationship Introduction Size effects in nanostructured (nanocrystalline, nanophase or nanocomposite) materials (NMs) are of great importance from both fundamental considerations and modern practice. The latter is connected with many things, e.g. the development of new NMs, selection of components for nanodevices and so on (1). This problem as a whole has been extensively analyzed in reviews (2,3); Arzt and Gleiter (4,5) have also discussed some important features. Within the limits of a short article, it is difficult to consider all aspects of size effects, therefore only so-me of them will be described herein as applied to consolidated NMs. General Considerations It seems of interest to consider the upper and lower limits of the NM grain sizes. By NMs, the materials are commonly meant in which the size of the grains or phases (D) composing their structure does not exceed 100 nm at least in one direction. This upper limit is very arbitrary and its value is dictated by convenience considerations rather than by physical ones. However, simple estimations show that, starting from this size, the fraction of disordered interface regions becomes increasingly noticeable (this fraction is about 3s/D, where s is the width of the grain-boundary region and D is the characteristic size); at reasonable values of s ⬵ 0.5–1 nm, the above fraction reaches several percent. On the other hand, as indicated originally (6), the upper limit of D should correspond to the size that is characteristic length of a physical phenomenon (e.g., the Frank-Read loop size for dislocation slip, the free path of carriers for transport properties, the domain features for magnetic characteristics, etc.). It is clear that the limiting D values would differ for different physical-chemical properties and different metals, alloys, semiconductors, compounds, etc. All these features determine the arbitrariness of the abovementioned limiting value of 100 nm. It is worth noting that the lower limit of the NM grain sizes can be about 1 nm. Such crystallites have been observed in Ti(B,N)X films prepared by magnetron sputtering (7). The lower limit of NMs, which may consists about several crystal units (23 ⫽ 8!), is near a cluster size and this case needs some special discussion (see, e.g. (2,5)). In materials science the effect of the grain size on the material properties is a long-explored problem. It is common knowledge that there are many relationships in this field such as the Hall-Petch equation, the Coble and Nabarro/Herring ones and so on. However, there are at least three principal features of 1359-6462/01/$–see front matter. © 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(01)00786-2
1622
SIZE EFFECTS IN PROPERTIES
Vol. 44, Nos. 8/9
size effects in NM. The first was mentioned above (overlapping of the grain size with the characteristic physical length). The second is the reduction of the crystallite size to the nanometer scale that implies an increase in the role of interfacial defects, i.e. grain boundaries, triple junctions, and elastically distorted layers. The third is that other structure and properties may characterize the grain boundaries of NM. The second and third features have been pointed out by Gleiter and many other authors (e.g. (8 –11)). In addition, from the viewpoint (12), the transition in the nanocrystalline state could be considered as a topological phenomenon in the ensemble of the grain-boundary defects which is accompanied by changing the connectivity. All these things may result in the presence of some specific points in the size dependencies and the availability of an unmonotonous change in the properties determined by the grain size decreasing. However, because of the small structural sensibility, the values of some thermal properties such as the heat capacity, the thermal expansion coefficient, etc., are in the good agreement with the data calculated on the basis of the “two-phase” description of the NM structure (2,5,8).
Specific Points in Size Dependencies. Some Complications Many authors (see, e.g. reviews (2–5) and other sources (13–20), have observed the abnormal structure-property relationships in NMs. This abnormality is that the values of microhardness, coercivity, permittivity and other decrease with reduction of the grain size. The most dramatic change is observed in the case of magnetic coercivity (HC) (13). Herzer (see Fig. 6 in (13)) pointed out that the grain size about 50 nm is the boundary between conventional relationship (HC⬃1/D) and that (HC ⬃ D6) for NMs. In the former case, the grain boundaries act as barriers for domain motion upon magnetization reversal and the theoretically predicted relationship HC ⬃ 1/D coincides with the experimental data obtained for the conventional polycrystalline magnets. In the latter case, the exchange interaction plays an essential role for randomly oriented nanograins; and the calculations predict the validity of the relationship HC ⬃D6 which is confirmed experimentally. Finally, the intermediate range, in which grains become comparable with interdomain spacing (the domain wall thickness ), and the maximum HC values are observed. In this case the value ⬃ 50 nm plays the role of the upper size limit for the nanocrystalline state. A few interesting examples of nanosize effects in electroceramics can be found in review (19). An unmonotonous change in the microhardness and other mechanical properties with reduction of the grain size has been detected in some NMs based on pure metals, alloys, nitride multilayers, and intermetallics (see e.g. (3–5,8,14 –18)). As a whole the principal seat of the changes such as the transition from the normal Hall-Petch relationship to the abnormal one, where microhardness decreases with reduction of the grain size, is not easy to explain and predict. However, it should be pointed that there are some special interesting models of grain-boundary microsliding, which may be used to explain the anomalies of the Hall-Petch relationship in NMs (3,17). In addition, the results of computersimulated deformation in nanocrystals revealed the availability of the anomalous Hall-Petch relationship (3,15,18). It is significant that compression and tensile testing of NMs revealed different values of their strength and, in particular, ductility. The study of hardness, fracture stress and ductility of warm-compacted nanocrystalline Fe powder compacts of a near theoretical density revealed that the values of hardness increased and those of fracture stress and elongation to failure decreased significantly with decreasing the grain size in the range from 33 to 8 nm (16). This is connected with the dramatic effect of processing defects such as flaws, micropores, etc., on the tensile values of strength. The presence of processing defects was confirmed by the SEM examination. Hence there are many reasons for masking size effects in NMs. In this connection the powder technology methods for defectless sample preparation seem to
Vol. 44, Nos. 8/9
SIZE EFFECTS IN PROPERTIES
1623
be less useful as compared with controlled crystallization from amorphous phase and the coating/film methods (PVD, CVD, and electrodeposition) (2,5,20,21). The processing history has a critical effect on the structure of interfaces in these subjects and the detail characterization by several independent methods is very important. The different features of the grain size determination by the X-ray diffraction and TEM examination as applied to nanostructured Pd samples have been discussed in detail by Krill and Birringer (22). The presence of impurities in NMs and their possible segregation on the grain boundaries may also change the property with reduction of the grain size. Especially as that, from general consideration and some calculations (see, e.g. (2)), the segregation effect must be intensified within the nanometer interval. Particular attention must be also given to the peculiarities of thermodynamics of very fine (cluster-assembled) NMs. The EDX and EELS investigations in this field seem to be very effective for the experimental study. Unfortunately, information on these results is not systematic and badly limited (2).
Conclusions We considered only some features of size effects in NMs. The authors directed the reader’s attention to the complexity of this problem. It seems to be likely that, despite a great body of information, the understanding of the nature of size effects in NMs is not so deep and the possibility of prediction in this field is limited. In addition, there are some complications in the preparation and characterization of representative samples. The knowledge of the size effect nature, in the context of fundamental significance and still incomplete data, requires intense further studies in order to highlight the best strategies for future technologies.
Acknowledgment R.A.A. wishes to point out that NATO’s Scientific Affairs Division in the framework of the Science sponsors the present research for Peace Program (Project No 973529).
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
M. C. Roco, R. S. Williams, and P. Alivisatos, ed., Nanotechnology Research Directions: IWGN Workshop Report (Vision for Nanotechnology in the Next Decade), p. 316, Kluwer Academic Publishers, Dordrecht (2000). R. A. Andrievski and A. M. Glezer, Phys. Met. Metallogr. 88(1), 45 (1999). R. A. Andrievski and A. M. Glezer, Phys. Met. Metallogr. 89(1), 91 (2000). E. Arzt, Acta Mater. 46, 5611 (1998). H. Gleiter, Acta Mater. 48, 1 (2000). I. D. Morokhov, V. I. Petinov, L. I. Trusov, and V. F. Petrunin, Uspekhi Fizicheskikh Nauk. 133, 655 (1981) (in Russian). R. A. Andrievski, G. V. Kalinnikov, and D. V. Shtansky, Phys. Solid State. 42, 741 (2000). H. Gleiter, Prog. Mater. Sci. 33, 223 (1989). G. Palumbo, S. J. Thorpe, and K. T. Aust, Scripta Metall. Mater. 24, 1347 (1990). R. Z. Valiev, A. V. Korznikov, and R. R. Mulyukov, Mater. Sci. Eng. 168A, 141 (1993). R. W. Siegel, J. Phys. Chem. Sol. 55, 1097 (1994). O. B. Neimark, Phys. Met. Metallogr. 84, 327 (1997). G. Herzer, IEEE Trans. Magn. MAG-26, 1397 (1990). B. M. Clement, H. Kung, and S. A. Barnett, MRS Bull. 24, 20 (1999). J. R. Weertman, D. Farkas, K. Hemker, H. Kung, M. Mayo, R. Mitra, and H. Van Swygenhoven, MRS Bull. 24, 44 (1999).
1624
16. 17. 18. 19. 20. 21. 22.
SIZE EFFECTS IN PROPERTIES
T. R. Malow and C. C. Koch, Acta Mater. 46, 6459 (1998). S. G. Zaichenko and A. M. Glezer, Mater. Sci. Forum. 269 –272, 687 (1998). J. Shiotz, F. D. Di Tolla, and K. W. Jacobsen, Nature. 391(5), 561 (1998). N. Setter and R. Waser, Acta Mater. 48, 151 (2000). K. Lu, Mater. Sci. Eng. Rep. 16, 161 (1996). A. Robertson, U. Erb, and G. Palumbo, Nanostruct. Mater. 12, 1035 (1999). C. E. Krill and R. Birringer, Phil. Mag. A. 77, 621 (1998).
Vol. 44, Nos. 8/9
SIZE EFFECTS IN PROPERTIES OF NANOMATERIALS R.A. Andrievski1 and A.M. Glezer2 1
Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, 142432 Russia 2Institute of Physical Metallurgy and Functional Materials, State Scientific Center, “I.P. Bardin Central Research Institute for the Iron/Steel Industry,” Moscow, 107005, Russia (Received August 21, 2000) (Accepted in revised form December 27, 2000)
Keywords: Nanostructured materials; Size effect; Structure-property relationship Introduction Size effects in nanostructured (nanocrystalline, nanophase or nanocomposite) materials (NMs) are of great importance from both fundamental considerations and modern practice. The latter is connected with many things, e.g. the development of new NMs, selection of components for nanodevices and so on (1). This problem as a whole has been extensively analyzed in reviews (2,3); Arzt and Gleiter (4,5) have also discussed some important features. Within the limits of a short article, it is difficult to consider all aspects of size effects, therefore only so-me of them will be described herein as applied to consolidated NMs. General Considerations It seems of interest to consider the upper and lower limits of the NM grain sizes. By NMs, the materials are commonly meant in which the size of the grains or phases (D) composing their structure does not exceed 100 nm at least in one direction. This upper limit is very arbitrary and its value is dictated by convenience considerations rather than by physical ones. However, simple estimations show that, starting from this size, the fraction of disordered interface regions becomes increasingly noticeable (this fraction is about 3s/D, where s is the width of the grain-boundary region and D is the characteristic size); at reasonable values of s ⬵ 0.5–1 nm, the above fraction reaches several percent. On the other hand, as indicated originally (6), the upper limit of D should correspond to the size that is characteristic length of a physical phenomenon (e.g., the Frank-Read loop size for dislocation slip, the free path of carriers for transport properties, the domain features for magnetic characteristics, etc.). It is clear that the limiting D values would differ for different physical-chemical properties and different metals, alloys, semiconductors, compounds, etc. All these features determine the arbitrariness of the abovementioned limiting value of 100 nm. It is worth noting that the lower limit of the NM grain sizes can be about 1 nm. Such crystallites have been observed in Ti(B,N)X films prepared by magnetron sputtering (7). The lower limit of NMs, which may consists about several crystal units (23 ⫽ 8!), is near a cluster size and this case needs some special discussion (see, e.g. (2,5)). In materials science the effect of the grain size on the material properties is a long-explored problem. It is common knowledge that there are many relationships in this field such as the Hall-Petch equation, the Coble and Nabarro/Herring ones and so on. However, there are at least three principal features of 1359-6462/01/$–see front matter. © 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(01)00786-2
1622
SIZE EFFECTS IN PROPERTIES
Vol. 44, Nos. 8/9
size effects in NM. The first was mentioned above (overlapping of the grain size with the characteristic physical length). The second is the reduction of the crystallite size to the nanometer scale that implies an increase in the role of interfacial defects, i.e. grain boundaries, triple junctions, and elastically distorted layers. The third is that other structure and properties may characterize the grain boundaries of NM. The second and third features have been pointed out by Gleiter and many other authors (e.g. (8 –11)). In addition, from the viewpoint (12), the transition in the nanocrystalline state could be considered as a topological phenomenon in the ensemble of the grain-boundary defects which is accompanied by changing the connectivity. All these things may result in the presence of some specific points in the size dependencies and the availability of an unmonotonous change in the properties determined by the grain size decreasing. However, because of the small structural sensibility, the values of some thermal properties such as the heat capacity, the thermal expansion coefficient, etc., are in the good agreement with the data calculated on the basis of the “two-phase” description of the NM structure (2,5,8).
Specific Points in Size Dependencies. Some Complications Many authors (see, e.g. reviews (2–5) and other sources (13–20), have observed the abnormal structure-property relationships in NMs. This abnormality is that the values of microhardness, coercivity, permittivity and other decrease with reduction of the grain size. The most dramatic change is observed in the case of magnetic coercivity (HC) (13). Herzer (see Fig. 6 in (13)) pointed out that the grain size about 50 nm is the boundary between conventional relationship (HC⬃1/D) and that (HC ⬃ D6) for NMs. In the former case, the grain boundaries act as barriers for domain motion upon magnetization reversal and the theoretically predicted relationship HC ⬃ 1/D coincides with the experimental data obtained for the conventional polycrystalline magnets. In the latter case, the exchange interaction plays an essential role for randomly oriented nanograins; and the calculations predict the validity of the relationship HC ⬃D6 which is confirmed experimentally. Finally, the intermediate range, in which grains become comparable with interdomain spacing (the domain wall thickness ), and the maximum HC values are observed. In this case the value ⬃ 50 nm plays the role of the upper size limit for the nanocrystalline state. A few interesting examples of nanosize effects in electroceramics can be found in review (19). An unmonotonous change in the microhardness and other mechanical properties with reduction of the grain size has been detected in some NMs based on pure metals, alloys, nitride multilayers, and intermetallics (see e.g. (3–5,8,14 –18)). As a whole the principal seat of the changes such as the transition from the normal Hall-Petch relationship to the abnormal one, where microhardness decreases with reduction of the grain size, is not easy to explain and predict. However, it should be pointed that there are some special interesting models of grain-boundary microsliding, which may be used to explain the anomalies of the Hall-Petch relationship in NMs (3,17). In addition, the results of computersimulated deformation in nanocrystals revealed the availability of the anomalous Hall-Petch relationship (3,15,18). It is significant that compression and tensile testing of NMs revealed different values of their strength and, in particular, ductility. The study of hardness, fracture stress and ductility of warm-compacted nanocrystalline Fe powder compacts of a near theoretical density revealed that the values of hardness increased and those of fracture stress and elongation to failure decreased significantly with decreasing the grain size in the range from 33 to 8 nm (16). This is connected with the dramatic effect of processing defects such as flaws, micropores, etc., on the tensile values of strength. The presence of processing defects was confirmed by the SEM examination. Hence there are many reasons for masking size effects in NMs. In this connection the powder technology methods for defectless sample preparation seem to
Vol. 44, Nos. 8/9
SIZE EFFECTS IN PROPERTIES
1623
be less useful as compared with controlled crystallization from amorphous phase and the coating/film methods (PVD, CVD, and electrodeposition) (2,5,20,21). The processing history has a critical effect on the structure of interfaces in these subjects and the detail characterization by several independent methods is very important. The different features of the grain size determination by the X-ray diffraction and TEM examination as applied to nanostructured Pd samples have been discussed in detail by Krill and Birringer (22). The presence of impurities in NMs and their possible segregation on the grain boundaries may also change the property with reduction of the grain size. Especially as that, from general consideration and some calculations (see, e.g. (2)), the segregation effect must be intensified within the nanometer interval. Particular attention must be also given to the peculiarities of thermodynamics of very fine (cluster-assembled) NMs. The EDX and EELS investigations in this field seem to be very effective for the experimental study. Unfortunately, information on these results is not systematic and badly limited (2).
Conclusions We considered only some features of size effects in NMs. The authors directed the reader’s attention to the complexity of this problem. It seems to be likely that, despite a great body of information, the understanding of the nature of size effects in NMs is not so deep and the possibility of prediction in this field is limited. In addition, there are some complications in the preparation and characterization of representative samples. The knowledge of the size effect nature, in the context of fundamental significance and still incomplete data, requires intense further studies in order to highlight the best strategies for future technologies.
Acknowledgment R.A.A. wishes to point out that NATO’s Scientific Affairs Division in the framework of the Science sponsors the present research for Peace Program (Project No 973529).
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
M. C. Roco, R. S. Williams, and P. Alivisatos, ed., Nanotechnology Research Directions: IWGN Workshop Report (Vision for Nanotechnology in the Next Decade), p. 316, Kluwer Academic Publishers, Dordrecht (2000). R. A. Andrievski and A. M. Glezer, Phys. Met. Metallogr. 88(1), 45 (1999). R. A. Andrievski and A. M. Glezer, Phys. Met. Metallogr. 89(1), 91 (2000). E. Arzt, Acta Mater. 46, 5611 (1998). H. Gleiter, Acta Mater. 48, 1 (2000). I. D. Morokhov, V. I. Petinov, L. I. Trusov, and V. F. Petrunin, Uspekhi Fizicheskikh Nauk. 133, 655 (1981) (in Russian). R. A. Andrievski, G. V. Kalinnikov, and D. V. Shtansky, Phys. Solid State. 42, 741 (2000). H. Gleiter, Prog. Mater. Sci. 33, 223 (1989). G. Palumbo, S. J. Thorpe, and K. T. Aust, Scripta Metall. Mater. 24, 1347 (1990). R. Z. Valiev, A. V. Korznikov, and R. R. Mulyukov, Mater. Sci. Eng. 168A, 141 (1993). R. W. Siegel, J. Phys. Chem. Sol. 55, 1097 (1994). O. B. Neimark, Phys. Met. Metallogr. 84, 327 (1997). G. Herzer, IEEE Trans. Magn. MAG-26, 1397 (1990). B. M. Clement, H. Kung, and S. A. Barnett, MRS Bull. 24, 20 (1999). J. R. Weertman, D. Farkas, K. Hemker, H. Kung, M. Mayo, R. Mitra, and H. Van Swygenhoven, MRS Bull. 24, 44 (1999).
1624
16. 17. 18. 19. 20. 21. 22.
SIZE EFFECTS IN PROPERTIES
T. R. Malow and C. C. Koch, Acta Mater. 46, 6459 (1998). S. G. Zaichenko and A. M. Glezer, Mater. Sci. Forum. 269 –272, 687 (1998). J. Shiotz, F. D. Di Tolla, and K. W. Jacobsen, Nature. 391(5), 561 (1998). N. Setter and R. Waser, Acta Mater. 48, 151 (2000). K. Lu, Mater. Sci. Eng. Rep. 16, 161 (1996). A. Robertson, U. Erb, and G. Palumbo, Nanostruct. Mater. 12, 1035 (1999). C. E. Krill and R. Birringer, Phil. Mag. A. 77, 621 (1998).
Vol. 44, Nos. 8/9