200
7 Nano-Mechanical Properties of Solid Surfaces Obtained …
of the anodic alumina film was employed for the determination of E s from the
measured E r . The value of H = 7.0 GPa obtained for the alumina film is significantly low as compared to H = 25.9 GPa for sapphire (111) [42], while it is higher
than that (H = 3 − 5 GPa) for the porous alumina film with an average thickness
of 744 nm on a glass substrate (H = 9 − 12 GPa) [43]. The high value of H for
the alumina film relative to the porous alumina film is attributed to the absence of
porosity. On the other hand, the significantly low value of H for the alumina film as
compared to sapphire (111) indicates that the anodic alumina film is soft relative to
crystalline forms.
The value of E s = 122 GPa for the anodic alumina film is lower by a factor of
3.2 or 3.5 than E s = 387 GPa for γ -Al 2 O 3 [44] or E s = 433 GPa for sapphire (111)
[42], which is matched by the low hardness value of the anodic alumina film. It has
been reported that Young’s modulus of γ -Al 2 O 3 decreases rapidly with increasing
humidity [44]. The low Young’s modulus of the anodic alumina film may result from
moisture absorbed or water remained in the film during anodic oxidation. The low
values of H and E s for the anodic alumina film afford proof that the anodic alumina
film is easily subjected to a plastic flow due to the evolution of compressive stress
during anodic oxidation of Al, which leads to the growth of the porous alumina layer
(see Sect. 6.9 of Chap. 6).
For comparison with the anodic alumina film, nano-indentation [41] was also
performed in the same shallow depth by using a Berkovich indenter for the anodic
oxide (tantala) film with a thickness of 408 ± 4 nm and for the mixed anodic oxide
(alumina/tantala) film with a thickness of 484 ± 4 nm, which were prepared with
anodic oxidation (at 5 mA cm
−2 in ammonium pentaborate solution) of sputterdeposited tantalum and Al-50 at% Ta alloy on Al foil substrate, respectively. The
values of H = 5.3 ± 0.5 GPa obtained for the anodic tantala film and of H =
6.5 ± 0.7 GPa obtained for the mixed anodic film are lower than that for the anodic
alumina film, while the values of E s = 140 ± 14 GPa for the anodic tantala film
and of E s = 130 ± 13 GPa for the mixed anodic film are higher than that for the
anodic alumina film. The hardness of the mixed anodic film is closer to that of the
anodic alumina film than that of the anodic tantala film, which is consistent with
the aluminum-enrichment in the outer layer (thicker than the indentation depth of
55 nm) of the mixed anodic film [46]. The anodic tantala films are amorphous by
X-ray diffraction, but they contain a local structure similar to β-Ta 2 O 5 [46, 47]. In
addition, the micro-diffraction by transmission electron microscopy (TEM) revealed
the presence of micro-crystallinity in the anodic tantala films [48]. On the other hand,
there is no information on the structure of the mixed oxide films.
The issue for determination of hardness and elastic modulus from the measured
load-depth curves is that the Oliver–Pharr method [1, 2] does not account for pileup of
material around the indenter impression as shown schematically in Fig. 7.16a. When
pileup occurs, the contact area is larger than that estimated by the Oliver–Pharr
method, and both hardness and elastic modulus determined by Eqs. (7.1) and (7.8)
are overestimated, sometimes by as much as 50% [49]. The Oliver–Pharr method is
based on an elastic contact analysis to estimate the contact depth. Since sink-in (see
Fig. 7.16b) always occurs for materials deformed elastically, pile-up cannot properly
7 Nano-Mechanical Properties of Solid Surfaces Obtained …
of the anodic alumina film was employed for the determination of E s from the
measured E r . The value of H = 7.0 GPa obtained for the alumina film is significantly low as compared to H = 25.9 GPa for sapphire (111) [42], while it is higher
than that (H = 3 − 5 GPa) for the porous alumina film with an average thickness
of 744 nm on a glass substrate (H = 9 − 12 GPa) [43]. The high value of H for
the alumina film relative to the porous alumina film is attributed to the absence of
porosity. On the other hand, the significantly low value of H for the alumina film as
compared to sapphire (111) indicates that the anodic alumina film is soft relative to
crystalline forms.
The value of E s = 122 GPa for the anodic alumina film is lower by a factor of
3.2 or 3.5 than E s = 387 GPa for γ -Al 2 O 3 [44] or E s = 433 GPa for sapphire (111)
[42], which is matched by the low hardness value of the anodic alumina film. It has
been reported that Young’s modulus of γ -Al 2 O 3 decreases rapidly with increasing
humidity [44]. The low Young’s modulus of the anodic alumina film may result from
moisture absorbed or water remained in the film during anodic oxidation. The low
values of H and E s for the anodic alumina film afford proof that the anodic alumina
film is easily subjected to a plastic flow due to the evolution of compressive stress
during anodic oxidation of Al, which leads to the growth of the porous alumina layer
(see Sect. 6.9 of Chap. 6).
For comparison with the anodic alumina film, nano-indentation [41] was also
performed in the same shallow depth by using a Berkovich indenter for the anodic
oxide (tantala) film with a thickness of 408 ± 4 nm and for the mixed anodic oxide
(alumina/tantala) film with a thickness of 484 ± 4 nm, which were prepared with
anodic oxidation (at 5 mA cm
−2 in ammonium pentaborate solution) of sputterdeposited tantalum and Al-50 at% Ta alloy on Al foil substrate, respectively. The
values of H = 5.3 ± 0.5 GPa obtained for the anodic tantala film and of H =
6.5 ± 0.7 GPa obtained for the mixed anodic film are lower than that for the anodic
alumina film, while the values of E s = 140 ± 14 GPa for the anodic tantala film
and of E s = 130 ± 13 GPa for the mixed anodic film are higher than that for the
anodic alumina film. The hardness of the mixed anodic film is closer to that of the
anodic alumina film than that of the anodic tantala film, which is consistent with
the aluminum-enrichment in the outer layer (thicker than the indentation depth of
55 nm) of the mixed anodic film [46]. The anodic tantala films are amorphous by
X-ray diffraction, but they contain a local structure similar to β-Ta 2 O 5 [46, 47]. In
addition, the micro-diffraction by transmission electron microscopy (TEM) revealed
the presence of micro-crystallinity in the anodic tantala films [48]. On the other hand,
there is no information on the structure of the mixed oxide films.
The issue for determination of hardness and elastic modulus from the measured
load-depth curves is that the Oliver–Pharr method [1, 2] does not account for pileup of
material around the indenter impression as shown schematically in Fig. 7.16a. When
pileup occurs, the contact area is larger than that estimated by the Oliver–Pharr
method, and both hardness and elastic modulus determined by Eqs. (7.1) and (7.8)
are overestimated, sometimes by as much as 50% [49]. The Oliver–Pharr method is
based on an elastic contact analysis to estimate the contact depth. Since sink-in (see
Fig. 7.16b) always occurs for materials deformed elastically, pile-up cannot properly