188
7 Nano-Mechanical Properties of Solid Surfaces Obtained …
70–175 nm were employed for the measurements of the load-depth curves for two
sets of the (111) / (001) and (111) / (110) surfaces. The values of E W = 411 GPa,
ν Au(111) = 0.44, ν Au(001) = 0.46, and ν Au(110) = 0.45 were used for determination of
E Au . The value of E Au(111) thus determined is 78–85 GPa, which is higher by about
36% than that of E Au(001) [6]. On the other hand, there was no statistically significant
difference between E Au(111) and E Au(110) .
The indentation modulus (78–85 GPa) of the Au (111) surface is close to Young’s
modulus (78.7 GPa) of a polycrystalline Au [15] and that (81.3 GPa) of a single crystal
Au (111) obtained from its elastic compliance data (see Sect. 3.2.3 of Chap. 3, and
Eqs. (4.18) ands (4.19) in Sect. 4.3.1 of Chap. 4). The effect of crystal orientation on
the indentation modulus of Au determined by using the parabolic tungsten indenter
[6] is greater than the theoretical results [8] of the indentation modulus calculated
by supposing the use of a rigid, flat, triangular indenter despite the same orientation
dependence of the indentation modulus. The difference in magnitude of the orientation effect may be ascribed to the difference in shape and size between the indenters
used for experiments [6].
Furthermore, the mean applied stresses σ p of the Au (111), (001), and (110)
surfaces were calculated by using Eq. (7.10) at the first deviation of the loading
curve from the Hertzian behavior or the onset point of discontinuity in the loading
curve. The calculated values of σ p are 7.3 GPa for the (111) orientation, 5.5 GPa
for the (001) orientation, and 7.8 GPa for the (110) orientation. In metals with facecentered cubic (fcc) structure such as Au, slip arises on closed-packed {111} planes
in 110 directions. Assuming an isotropic Hertzian stress distribution, the maximum
shear stresses on {111}}110 slip systems were resolved for each of the orientations,
and the resolved shear stress τ c on the
1 ¯
1 ¯
1
¯
10 ¯
1
slip system at the initial yielding
point was estimated by multiplying the measured mean applied stresses σ p with
their fractions (about half of 0.465 in Eq. (7.12)) predicted from the Hertzian stress
distribution. The estimated value of τ c on the
1 ¯
1 ¯
1
¯
10 ¯
1
slip system is about 1.8
GPa, irrespective of orientations. The estimated value of τ c ranges in the same level
as the results obtained by other researchers [7, 12, 16] if the measured values of σ p
are resolved to the shear components.
Nano-indentation of single crystal Au (100) thin films on NaCl substrate has been
performed to explore the effect of film thickness on hardness and elastic modulus
as well as on the initial plastic deformation [14]. The Au (100) thin films in the
range of 32–858 nm were deposited on cleaved and polished (100) oriented NaCl
single-crystalline substrates by magnetron sputtering. At first, the load-depth curves
with partial unloading cycles were measured for the Au (100) thin films on NaCl
substrate by using a Berkovich tip with a tip radius of 200 nm as exemplified in
Fig. 7.8 [14]. The values of reduced indentation modulus E r and hardness H were
determined as a function of indentation depth from the partial unloading curves by
applying the Oliver–Pharr method (see Eqs. (7.1)–(7.8)). Both the values of E r and
H decrease with increasing indentation depth, independent of the film thickness. As
the indentation depth approaches the Au/NaCl interface, the value of E r attains to
that (E r = 43 GPa) of the NaCl substrate. The values of E r , E s , and H obtained from
the partial unloading curves at indentation depths of 10 and 20% of the film thickness
7 Nano-Mechanical Properties of Solid Surfaces Obtained …
70–175 nm were employed for the measurements of the load-depth curves for two
sets of the (111) / (001) and (111) / (110) surfaces. The values of E W = 411 GPa,
ν Au(111) = 0.44, ν Au(001) = 0.46, and ν Au(110) = 0.45 were used for determination of
E Au . The value of E Au(111) thus determined is 78–85 GPa, which is higher by about
36% than that of E Au(001) [6]. On the other hand, there was no statistically significant
difference between E Au(111) and E Au(110) .
The indentation modulus (78–85 GPa) of the Au (111) surface is close to Young’s
modulus (78.7 GPa) of a polycrystalline Au [15] and that (81.3 GPa) of a single crystal
Au (111) obtained from its elastic compliance data (see Sect. 3.2.3 of Chap. 3, and
Eqs. (4.18) ands (4.19) in Sect. 4.3.1 of Chap. 4). The effect of crystal orientation on
the indentation modulus of Au determined by using the parabolic tungsten indenter
[6] is greater than the theoretical results [8] of the indentation modulus calculated
by supposing the use of a rigid, flat, triangular indenter despite the same orientation
dependence of the indentation modulus. The difference in magnitude of the orientation effect may be ascribed to the difference in shape and size between the indenters
used for experiments [6].
Furthermore, the mean applied stresses σ p of the Au (111), (001), and (110)
surfaces were calculated by using Eq. (7.10) at the first deviation of the loading
curve from the Hertzian behavior or the onset point of discontinuity in the loading
curve. The calculated values of σ p are 7.3 GPa for the (111) orientation, 5.5 GPa
for the (001) orientation, and 7.8 GPa for the (110) orientation. In metals with facecentered cubic (fcc) structure such as Au, slip arises on closed-packed {111} planes
in 110 directions. Assuming an isotropic Hertzian stress distribution, the maximum
shear stresses on {111}}110 slip systems were resolved for each of the orientations,
and the resolved shear stress τ c on the
1 ¯
1 ¯
1
¯
10 ¯
1
slip system at the initial yielding
point was estimated by multiplying the measured mean applied stresses σ p with
their fractions (about half of 0.465 in Eq. (7.12)) predicted from the Hertzian stress
distribution. The estimated value of τ c on the
1 ¯
1 ¯
1
¯
10 ¯
1
slip system is about 1.8
GPa, irrespective of orientations. The estimated value of τ c ranges in the same level
as the results obtained by other researchers [7, 12, 16] if the measured values of σ p
are resolved to the shear components.
Nano-indentation of single crystal Au (100) thin films on NaCl substrate has been
performed to explore the effect of film thickness on hardness and elastic modulus
as well as on the initial plastic deformation [14]. The Au (100) thin films in the
range of 32–858 nm were deposited on cleaved and polished (100) oriented NaCl
single-crystalline substrates by magnetron sputtering. At first, the load-depth curves
with partial unloading cycles were measured for the Au (100) thin films on NaCl
substrate by using a Berkovich tip with a tip radius of 200 nm as exemplified in
Fig. 7.8 [14]. The values of reduced indentation modulus E r and hardness H were
determined as a function of indentation depth from the partial unloading curves by
applying the Oliver–Pharr method (see Eqs. (7.1)–(7.8)). Both the values of E r and
H decrease with increasing indentation depth, independent of the film thickness. As
the indentation depth approaches the Au/NaCl interface, the value of E r attains to
that (E r = 43 GPa) of the NaCl substrate. The values of E r , E s , and H obtained from
the partial unloading curves at indentation depths of 10 and 20% of the film thickness