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Evaluation of mechanical properties in nanometer scale using AFM-based nanoindentation tester
NaooStmctured Materials, Vol. 12, pp. 1049-1052, 1999 Elsevier Science Ltd Q 1999 Acta Metallurgica Inc. tinted in the USA. All rights reserved 09659713l996-see front matter
Pergamon
PI1 SO%59773(99)00297-4
EVALIJATION OF MECHANICAL PROPERTIES IN NANOMETER SCALE USING AFM-BASED NANOINDENTATION TESTER K. Miyahara,
N. Nagashima,
T. Ohmura, aud S. Matsuoka
National Research Institute for Metals 1-2-1 Sengen, Tsukuba-shi, Ibaraki 3050047, Japan Abstract -A nanoindentation hardness tester was developed on the basis of an atomic force microscope (AM) to evaluate mechanical properties of microstructures. Not only the force penetration depth curves but the topographic images can be obtained by this tester One of new features of the developed tester was modified lever design in order to accommodate the Berkovich indenter into the middle of the lever Furthermore, a piezo-actuator was added to control the appliedforce and the vertical displacement of the lever was monitored by a laser displacement detector Tlhediamond tip works as both an AFM tip and indenter Force -penetration depth curves represent mechanical properties of specimens. However; because of indentation size eflect, the hardness values obtained by nanoindentation testers are usually greater than the bulk harhess. In this paper several metallic single crystals were used as standard specimens and an empirical model for calculating tickers hardness from force penetration depth curves is proposed. Finally, mechanical properties of ferrite in pearlitic steels were #obtainedusing the instrument. 01999 Acta Metallurgica Inc.
INTRODUCTION
The evaluation of mechanical properties in microstrnctures becomes much more important as a result of increasing interests in nanostructured materials, semiconductor devices, and suucmml materials. Nanoindentation hardness testers, which have been developed and studied intensive nowadays (1,2,3), can provide such information. In this paper a new AFM-based nanoindent,ation tester is introduced and a simple method to evaluate Vickers hardness from force - penetration depth curves is proposed.
AFM-BASED
NANOINDENTATION
TESTER
Figure 11shows a diagram of the AFM-based nanoindentation tester and its special lever developed by the authors. The difference from a conventional atomic force microscope is as follows: (a) use of a special lever held on both sides, (b) addition of a piezo-actuator for force control, and (c) measurement of lever displacement instead of its deflection. Further details of this instrument are described elsewhere (1). It should be noted that both force - penetration 1049
1050
FOURTH INTERNATIONAL CONFERENCEON NAN~STRUCTUREDMATERIALS
depth curves and surface topographic images are easily available with this system. Indentation experiments were carried out under force control mode. Loading and unloading rate was 10 @J/s for all experiments. AFM images were obtained before and after indentation test in order to choose flat location for hardness test and observe indentation shape. A Berkovich diamond indenter with an apical angle of 60“ was used, to obtain sharp AFM images. In hardness tests, the indentation size effect (ISE) is often observed, i.e., the hardness values obtained by nanoindentation testers are usually greater than the bulk hardness. In order to apply this instrument to material research, it is desirable to measure an ‘absolute’ hardness value, which is independent of experimental conditions such as curvature radius of indenters and free from the ISE. Empirical methods are necessary for this purpose because whether the ISE is a genuine size effect or not is still under discussion (2) and to estimate effects of indenter roundness and specimen surface analytically and quantitatively is still not easy when penetration depth is as low as 100 mu. Oliver et al. (3) proposed a new technique for determining hardness and elastic modulus by correcting contact area to reduce the indentation size effect. In this work, a simple empirical method for evaluating hardness with reduced indentation size effect is proposed and described in the following section.
EXPERIMENTAL
RESULTS AND DISCUSSION
The (100) surfaces of single crystals of tungsten, molybdenum, iron and nickel were used as test specimens. These specimens were polished mechanically and then electrolytically. They are used as standard specimens for determining hardness. The basic idea of hardness determination is to establish the relationship between macroscopic hardness and force penetration depth curves in nanoindentation. The single crystals were used since they have no grain boundaries or precipitates and therefore the same mechanical properties would be expected in both nanoindentation and macroscopic hardness tests. Figure 2 shows force - penetration depth curves of the single crystals. It can be seen from Fig. 2 that at the same force level, the depth of indentation decreases as the degree of Vickers hardness increases. This means relative hardness can be compared in any case. Figure 3 shows Laser
DisplacementDetector h
Piezo Transducer
Diamond Indenter
\ Piem Scanner
Fig. 1 AFM-based nanoindentation tester and its special lever.
FOURTH INTERNATIONAL CONFERENCEON NANOSTRUCTURED MATERIALS
1051
the relationship between force necessary to achieve a certain penetration depth and Vickers hardness obtained by a conventional Vickers hardness tester at 100 gf. Using standard curve fitting technique, a power function model was found to be the best one to describe the relationship. This power faction is shown in the following equation: (h >lOO)
HV = [a(h) FJ n
PI
where HV is Vickers hardness, F is force in pN, and h is penetration depth in nm. a(h) is hdependent and n is a constant and n = 1.214 in this case. Plotting F(h)/WV */nagainst h further and again using curve-fitting for various type of functions, the best fitted one was found as: (h > 100)
PI
wherep = 5.6634 x 10 -3and q = 122.83. Subsequently, Eq. [2] can be rewritten in terms of HV as follows:
= [F/ IS.6634
x 10 -3(h f 122.83)‘)] 1.214 (h > 100)
[31
It should be noted that these parameters may be valid only for the current indenter and their physical melmings are not clear yet. However, a possible hypothesis is that q represents the truncation length of indenter and p and n are related to hardness conversion between 60“ indenter and Vickers indenter. Further experiments and discussion will be necessary. A pearlitic steel was chosen as a test material. The pearlitic steel was etched by 1% nitric acid and 99% alcohol. The microstructure of the pearlitic steel, i.e., ferrite grains and cementite lamellae, is in submicron scale as shown in the AFM image in Fig. 4. The mechanical properties of the micro:structure are much of interest in order to establish a model in micromechanics. ltim
2CCnm
4COnm
Penetration Depth (nm)
Fig. 2 Force - penetration depth curves of single crystals.
Force ( p N)
Fig. 3 Relationship between force and Vickers hardness of single crystals
1052
FOURTHINTERNATIONAL CONFERENCE ONNANOSTRUCTURED MATERIALS
Fig. 4 AFM image of an indentation on ferrite 0 50 loo 150 200 250 Penetration Depth (run) in pearlitic steels Fig. 5 Force - penetration depth curves of ferrite. Figure 4 illustrates an indentation on a ferrite grain. Because of imaging capability of the instrument, it is easy to choose a specific location for nanoindentation tests even if a specimen is heterogeneous. Figure 5 shows force - penetration depth curves for both pearlitic and ferritic steels. Both curves showed almost the same properties. A slight difference was observed at 200 mn, which might be due to cementite lamellae. From Fig. 5 and Eq. [3], Vickers hardness is estimated as 160 - 170 and it is greater than 98, which is the value of the iron single crystal. This difference may be due to the effect of dislocations and chemical composition. It’s worth noting that there is a discontinuation in force - penetration depth curves shown in Fig. 5. This behavior can be observed in Fig. 2, too. It is considered as a yield point and consistent with the results reported previously (3,4,5).
CONCLUSION An AFM-based nanoindentation tester was successfully developed, which allows both force - penetration depth curves and AFM topographic images to be obtained. A simple empirical method to evaluate Vickers hardness from force curves was proposed and mechanical properties of pearlitic and ferritic steels were obtained, using the developed tester and proposed method.
REFERENCES (1) Miyahara, K., Matsuoka, S., Nagashima, N. and Mishima, S., Trans. Jpn. Sot. Mech. Eng. A, fl(1995), pp. 2321-2328. (2) Tabor, D., Phil. Mag. A, 74 (1996), pp. 1207-1212. (3)Oliver, W. C. and Pharr, G. M., J. Mater. Rex, 1(1992), pp. 1564-1583. (4) Gerberich, W. W., Nelson, J. C., Lilleodden, E. T., Anderson, P. and Wyrobek, J. T., Acta metal., 44 (1996), pp. 3538-3598. (5) Miyahara, K., Matsuoka, S and Nagashima, N., Trans. Jpn. Sot. Mech. Eng. A, 63 (1997), pp. 2220-2227.
Pergamon
PI1 SO%59773(99)00297-4
EVALIJATION OF MECHANICAL PROPERTIES IN NANOMETER SCALE USING AFM-BASED NANOINDENTATION TESTER K. Miyahara,
N. Nagashima,
T. Ohmura, aud S. Matsuoka
National Research Institute for Metals 1-2-1 Sengen, Tsukuba-shi, Ibaraki 3050047, Japan Abstract -A nanoindentation hardness tester was developed on the basis of an atomic force microscope (AM) to evaluate mechanical properties of microstructures. Not only the force penetration depth curves but the topographic images can be obtained by this tester One of new features of the developed tester was modified lever design in order to accommodate the Berkovich indenter into the middle of the lever Furthermore, a piezo-actuator was added to control the appliedforce and the vertical displacement of the lever was monitored by a laser displacement detector Tlhediamond tip works as both an AFM tip and indenter Force -penetration depth curves represent mechanical properties of specimens. However; because of indentation size eflect, the hardness values obtained by nanoindentation testers are usually greater than the bulk harhess. In this paper several metallic single crystals were used as standard specimens and an empirical model for calculating tickers hardness from force penetration depth curves is proposed. Finally, mechanical properties of ferrite in pearlitic steels were #obtainedusing the instrument. 01999 Acta Metallurgica Inc.
INTRODUCTION
The evaluation of mechanical properties in microstrnctures becomes much more important as a result of increasing interests in nanostructured materials, semiconductor devices, and suucmml materials. Nanoindentation hardness testers, which have been developed and studied intensive nowadays (1,2,3), can provide such information. In this paper a new AFM-based nanoindent,ation tester is introduced and a simple method to evaluate Vickers hardness from force - penetration depth curves is proposed.
AFM-BASED
NANOINDENTATION
TESTER
Figure 11shows a diagram of the AFM-based nanoindentation tester and its special lever developed by the authors. The difference from a conventional atomic force microscope is as follows: (a) use of a special lever held on both sides, (b) addition of a piezo-actuator for force control, and (c) measurement of lever displacement instead of its deflection. Further details of this instrument are described elsewhere (1). It should be noted that both force - penetration 1049
1050
FOURTH INTERNATIONAL CONFERENCEON NAN~STRUCTUREDMATERIALS
depth curves and surface topographic images are easily available with this system. Indentation experiments were carried out under force control mode. Loading and unloading rate was 10 @J/s for all experiments. AFM images were obtained before and after indentation test in order to choose flat location for hardness test and observe indentation shape. A Berkovich diamond indenter with an apical angle of 60“ was used, to obtain sharp AFM images. In hardness tests, the indentation size effect (ISE) is often observed, i.e., the hardness values obtained by nanoindentation testers are usually greater than the bulk hardness. In order to apply this instrument to material research, it is desirable to measure an ‘absolute’ hardness value, which is independent of experimental conditions such as curvature radius of indenters and free from the ISE. Empirical methods are necessary for this purpose because whether the ISE is a genuine size effect or not is still under discussion (2) and to estimate effects of indenter roundness and specimen surface analytically and quantitatively is still not easy when penetration depth is as low as 100 mu. Oliver et al. (3) proposed a new technique for determining hardness and elastic modulus by correcting contact area to reduce the indentation size effect. In this work, a simple empirical method for evaluating hardness with reduced indentation size effect is proposed and described in the following section.
EXPERIMENTAL
RESULTS AND DISCUSSION
The (100) surfaces of single crystals of tungsten, molybdenum, iron and nickel were used as test specimens. These specimens were polished mechanically and then electrolytically. They are used as standard specimens for determining hardness. The basic idea of hardness determination is to establish the relationship between macroscopic hardness and force penetration depth curves in nanoindentation. The single crystals were used since they have no grain boundaries or precipitates and therefore the same mechanical properties would be expected in both nanoindentation and macroscopic hardness tests. Figure 2 shows force - penetration depth curves of the single crystals. It can be seen from Fig. 2 that at the same force level, the depth of indentation decreases as the degree of Vickers hardness increases. This means relative hardness can be compared in any case. Figure 3 shows Laser
DisplacementDetector h
Piezo Transducer
Diamond Indenter
\ Piem Scanner
Fig. 1 AFM-based nanoindentation tester and its special lever.
FOURTH INTERNATIONAL CONFERENCEON NANOSTRUCTURED MATERIALS
1051
the relationship between force necessary to achieve a certain penetration depth and Vickers hardness obtained by a conventional Vickers hardness tester at 100 gf. Using standard curve fitting technique, a power function model was found to be the best one to describe the relationship. This power faction is shown in the following equation: (h >lOO)
HV = [a(h) FJ n
PI
where HV is Vickers hardness, F is force in pN, and h is penetration depth in nm. a(h) is hdependent and n is a constant and n = 1.214 in this case. Plotting F(h)/WV */nagainst h further and again using curve-fitting for various type of functions, the best fitted one was found as: (h > 100)
PI
wherep = 5.6634 x 10 -3and q = 122.83. Subsequently, Eq. [2] can be rewritten in terms of HV as follows:
= [F/ IS.6634
x 10 -3(h f 122.83)‘)] 1.214 (h > 100)
[31
It should be noted that these parameters may be valid only for the current indenter and their physical melmings are not clear yet. However, a possible hypothesis is that q represents the truncation length of indenter and p and n are related to hardness conversion between 60“ indenter and Vickers indenter. Further experiments and discussion will be necessary. A pearlitic steel was chosen as a test material. The pearlitic steel was etched by 1% nitric acid and 99% alcohol. The microstructure of the pearlitic steel, i.e., ferrite grains and cementite lamellae, is in submicron scale as shown in the AFM image in Fig. 4. The mechanical properties of the micro:structure are much of interest in order to establish a model in micromechanics. ltim
2CCnm
4COnm
Penetration Depth (nm)
Fig. 2 Force - penetration depth curves of single crystals.
Force ( p N)
Fig. 3 Relationship between force and Vickers hardness of single crystals
1052
FOURTHINTERNATIONAL CONFERENCE ONNANOSTRUCTURED MATERIALS
Fig. 4 AFM image of an indentation on ferrite 0 50 loo 150 200 250 Penetration Depth (run) in pearlitic steels Fig. 5 Force - penetration depth curves of ferrite. Figure 4 illustrates an indentation on a ferrite grain. Because of imaging capability of the instrument, it is easy to choose a specific location for nanoindentation tests even if a specimen is heterogeneous. Figure 5 shows force - penetration depth curves for both pearlitic and ferritic steels. Both curves showed almost the same properties. A slight difference was observed at 200 mn, which might be due to cementite lamellae. From Fig. 5 and Eq. [3], Vickers hardness is estimated as 160 - 170 and it is greater than 98, which is the value of the iron single crystal. This difference may be due to the effect of dislocations and chemical composition. It’s worth noting that there is a discontinuation in force - penetration depth curves shown in Fig. 5. This behavior can be observed in Fig. 2, too. It is considered as a yield point and consistent with the results reported previously (3,4,5).
CONCLUSION An AFM-based nanoindentation tester was successfully developed, which allows both force - penetration depth curves and AFM topographic images to be obtained. A simple empirical method to evaluate Vickers hardness from force curves was proposed and mechanical properties of pearlitic and ferritic steels were obtained, using the developed tester and proposed method.
REFERENCES (1) Miyahara, K., Matsuoka, S., Nagashima, N. and Mishima, S., Trans. Jpn. Sot. Mech. Eng. A, fl(1995), pp. 2321-2328. (2) Tabor, D., Phil. Mag. A, 74 (1996), pp. 1207-1212. (3)Oliver, W. C. and Pharr, G. M., J. Mater. Rex, 1(1992), pp. 1564-1583. (4) Gerberich, W. W., Nelson, J. C., Lilleodden, E. T., Anderson, P. and Wyrobek, J. T., Acta metal., 44 (1996), pp. 3538-3598. (5) Miyahara, K., Matsuoka, S and Nagashima, N., Trans. Jpn. Sot. Mech. Eng. A, 63 (1997), pp. 2220-2227.