190
7 Nano-Mechanical Properties of Solid Surfaces Obtained …
with a tip radius of 700 nm. The values of E r,Hertz in the fourth column of Table 7.1
[14] were determined from the Hertz fit (see Eq. (7.9)) of the elastic portion in the
measured loading curves. In contrast to E r and E s , E r,Hertz increases steadily with
increasing film thickness. The difference between E r and E r,Hertz may result from
the difference in indentation depth (5–10 nm for E r,Hertz and 13–170 nm for E r ) in
addition to the difference in experimental procedure. The hardness of a film/substrate
system depends on the substrate as well as indentation depth [14]. The increase in
H from 1.07 (0.71) GPa to 2.79 (1.81) GPa with decreasing film thickness from 858
to 207 nm in Table 7.1 may be explained in terms of the indentation size effect (ISE)
[17] and of the constraint in the dislocation motion at the film/substrate interface
[18–20]. On the other hand, the decrease in H at a film thickness of 134 nm is
ascribed to an additional plastic deformation in the NaCl substrate because of a
distinct displacement excursion observed for a film thickness of 134 nm at a load of
about 160 µN [14], corresponding to dislocation burst in the substrate. According to
the nano-indentation study [12] of the single crystal Au (100) surface achieved by
using a Berkovich tip with a 205 nm radius, the value of H increases from 0.6 to 2
GPa as the indentation depth decreases below 50 nm. Similarly, the ISE study [21]
of face-centered cubic (fcc) single crystal metals indicated that the value of H for
the single crystal Au (100) surface increases from 1.2 to 1.8 GPa as the indentation
depth decreases below 50 nm.
7.3.2 Metal Oxide Surfaces
We discuss the nano-mechanical properties of single crystal TiO 2 and magnetite
surfaces as typical results of nano-indentation on bulk metal oxide surfaces. A Nb
(0.05 wt%)-doped rutile type of TiO 2 (001) crystal wafer (a diameter of 10 mm and a
thickness of 3 mm) with an epi-polished surface was prepared for nano-indentation.
The separate single indentations on the different surface positions of the TiO 2 (001)
crystal wafer were achieved 20 times at each maximum load (up to L max = 3000 μN)
by using a Berkovich tip, and the measured load-depth curves were averaged at each
maximum load. Figure 7.9 shows the averaged load-depth curves in the depth range
less than 100 nm. The hardness values H determined from the averaged load-depth
curves by the Oliver–Pharr method [1, 2] are plotted versus the contact depth h c in
Fig. 7.10. The constant value of H = 14 ± 1 GPa is obtained in the contact depth
range of h c = 20 − 100 nm for the TiO 2 (001) surface except for H ≈ 10 GPa at
h c ≈ 10 nm. Figure 7.11 shows the relationship between S
−1 and A
−
1
2 . The reduced
indentation modulus E r = 316 GPa is obtained from the slope (2.80 × 10
−12 Pa
−1 )
of the linear relationship in Fig. 7.11. If Poisson’s ratio ν TiO 2 = 0.25 is employed
[22], the indentation modulus, i.e., Young’s modulus E s = 409 GPa is obtained
for the TiO 2 (001) surface. The values of H = 14 ± 1 GPa and E s = 409 GPa
obtained by nano-indention for the TiO 2 (001) surface are significantly higher than
the micro-hardness of H = 6 − 8 GPa at a maximum load of L max = 0.5 − 1.0 N
and Young’s modulus E s = 88.2 GPa for a polycrystalline TiO 2 [23].
7 Nano-Mechanical Properties of Solid Surfaces Obtained …
with a tip radius of 700 nm. The values of E r,Hertz in the fourth column of Table 7.1
[14] were determined from the Hertz fit (see Eq. (7.9)) of the elastic portion in the
measured loading curves. In contrast to E r and E s , E r,Hertz increases steadily with
increasing film thickness. The difference between E r and E r,Hertz may result from
the difference in indentation depth (5–10 nm for E r,Hertz and 13–170 nm for E r ) in
addition to the difference in experimental procedure. The hardness of a film/substrate
system depends on the substrate as well as indentation depth [14]. The increase in
H from 1.07 (0.71) GPa to 2.79 (1.81) GPa with decreasing film thickness from 858
to 207 nm in Table 7.1 may be explained in terms of the indentation size effect (ISE)
[17] and of the constraint in the dislocation motion at the film/substrate interface
[18–20]. On the other hand, the decrease in H at a film thickness of 134 nm is
ascribed to an additional plastic deformation in the NaCl substrate because of a
distinct displacement excursion observed for a film thickness of 134 nm at a load of
about 160 µN [14], corresponding to dislocation burst in the substrate. According to
the nano-indentation study [12] of the single crystal Au (100) surface achieved by
using a Berkovich tip with a 205 nm radius, the value of H increases from 0.6 to 2
GPa as the indentation depth decreases below 50 nm. Similarly, the ISE study [21]
of face-centered cubic (fcc) single crystal metals indicated that the value of H for
the single crystal Au (100) surface increases from 1.2 to 1.8 GPa as the indentation
depth decreases below 50 nm.
7.3.2 Metal Oxide Surfaces
We discuss the nano-mechanical properties of single crystal TiO 2 and magnetite
surfaces as typical results of nano-indentation on bulk metal oxide surfaces. A Nb
(0.05 wt%)-doped rutile type of TiO 2 (001) crystal wafer (a diameter of 10 mm and a
thickness of 3 mm) with an epi-polished surface was prepared for nano-indentation.
The separate single indentations on the different surface positions of the TiO 2 (001)
crystal wafer were achieved 20 times at each maximum load (up to L max = 3000 μN)
by using a Berkovich tip, and the measured load-depth curves were averaged at each
maximum load. Figure 7.9 shows the averaged load-depth curves in the depth range
less than 100 nm. The hardness values H determined from the averaged load-depth
curves by the Oliver–Pharr method [1, 2] are plotted versus the contact depth h c in
Fig. 7.10. The constant value of H = 14 ± 1 GPa is obtained in the contact depth
range of h c = 20 − 100 nm for the TiO 2 (001) surface except for H ≈ 10 GPa at
h c ≈ 10 nm. Figure 7.11 shows the relationship between S
−1 and A
−
1
2 . The reduced
indentation modulus E r = 316 GPa is obtained from the slope (2.80 × 10
−12 Pa
−1 )
of the linear relationship in Fig. 7.11. If Poisson’s ratio ν TiO 2 = 0.25 is employed
[22], the indentation modulus, i.e., Young’s modulus E s = 409 GPa is obtained
for the TiO 2 (001) surface. The values of H = 14 ± 1 GPa and E s = 409 GPa
obtained by nano-indention for the TiO 2 (001) surface are significantly higher than
the micro-hardness of H = 6 − 8 GPa at a maximum load of L max = 0.5 − 1.0 N
and Young’s modulus E s = 88.2 GPa for a polycrystalline TiO 2 [23].