Moreover, the interface between amorphous coating and the AZ31 substrate seems to be
tightly bound through physical contact, since no obvious crystalline diffraction peak of any
reactive phase formed by the reactions is observed.
4-2
Microhardness and Nanoindentation tests of Pd
77Cu
6Si
17TFMGs on
AZ31
Before the microhardness test, the roughness and surface topography of the AZ31
substrate were examined using atomic force microscopy (AFM) as shown in Figure 4-3 (a)
and Figure 4-4 (a). The roughness (Ra) is ~70 nm and ~10 nm under surface treatments of
diamond paste polishing and SiO2 polishing, respectively. Figure 4-3 (b) and Figure 4-4 (b)
are their morphologies taken by optical microscopy (OM). Despite the difference in
roughness, the substrates exhibit almost the same hardness in microhardness test. The
hardness is insensitive to the 10-70 nm roughness in this range under microhardness testing.
Although it is easier to prevent the samples from pollutions, surface oxidation of the
AZ31 substrate is unavoidable in the procedure of mechanical polishing. In our previous
results [71], the hardness datum base for the AZ31 substrate has been set up. Taking some
parameters into the Hall-Petch relationship, the hardness can be well followed using the
following equation:
Hv = 40 + 72 d 2
−1
, (4-1)
where Hv is the hardness, and d is the average grain size. The average grain size of the current
AZ31 substrate estimated from Figure 4-5 is ~60 µm. Taking the average size of ~60 µm into
the equation 4-1, Hv is 49. The measured hardness of the AZ31 substrate after mechanical
polishing is ~53 Hv, which can be transformed into 0.52 GPa. It could be inferred that the
oxidation of the AZ31 substrate also had no strong effect on hardness.
Microhardness testing provides a simple way to examine if the TFMGs would toughen
the AZ31 substrate. The cracks of PCS resulted from the applied loads may cause unclear
indentation marks under OM observation. The high-resolution measurement for indentation
mark can be accomplished under SEM observation. To obtain the accurate hardness values of
TFMGs, we measured the indentation marks of the deformed samples and estimate the
hardness based on the standard hardness equation. The equation of Vickers microhardness
measurement can be expressed as [53],
2
) 2 ( sin / 102 2 . 0 102
. 0
H d
F S
F
v α
×
=
×
= , (4-2)
where F is the applied loading, S is the area of indentation mark, α is the face-to-face angle,
equal to 136o of Vickers tip, and d is the average length of the diagonal lines caused by tip,
respectively. Using the value of d accurately measured from SEM observation and all known
parameters, the hardness can be calculated.
For the convenience of expressing the indented behavior, the penetration depth of indent
(d) over the film thickness (t), namely, d/t, is denoted as β. For the microhardness test, the
ratio is more than 1 for all the cases, from 1.25 up to 11. For nanoindentation, β varies from
0.05 to 2.0. The hardness measurements and percentages of enhancement from microhardness
and nanoindentation tests are shown in Figure 4-6, 4-7, and 4-8.
When the penetration depth is limited in the shallow region, the enhancement of
apparent hardness can be more than 100% due to the protection of hard TFMG. Subsequently,
the hardness decreases with increasing β ratio. In the β range between 1 and 2, hardness
drops down rapidly because of the rising contribution of AZ31 substrate. The enhancement of
TFMG to the whole material becomes less and less. When β is over 2.0, the hardness of the
AZ31 substrate starts to dominate the whole system. As a result, the decreasing tendency of
hardness slows down in the range of 2.0 < β < 11, approaching to the hardness of AZ31
substrate gradually. It is noticed that the two microhardness-β curves for PCS-1000 and
PCS-2000 match well, as shown in Figure 4-6. The current results demonstrate that the
hardness of coated specimen is insensitive to the thickness of TFMGs. The β ratio appears to
be the key parameter in determining the system hardness.
For nanoindentation, the indented β ratio is limited within 2.0 as shown in Figure 4-7.
Due to the dominant role of TFMG, the nanoindentation hardness readings are mostly higher
than 2 GPa, significantly higher than the AZ31 substrate, 0.52 GPa. Though the indenter tips
for microhardness and nanoindentation are not the same, the trends of hardness-β curves
obtained from these two test are still combined for comparison, as presented in Figure 4-8. It
is evident that the basic variation trend of the hardness as a function of β ratio from the nano
to micron range is similar.
4-3
Hardness marks of Pd
77Cu
6Si
17contings on AZ31
The indentation mark of AZ31 substrate is shown in Figure 4-9. We here use the
PCS-2000 as the example to demonstrate the indented surface morphology. PCS-2000 at
β~1.25 exhibits another type of morphology, as shown in Figure 4-10 (a). Compared with the
AZ31 substrate, the surface becomes smoother after coating. Based on the inclined sides of
the microhardness marks in Figure 4-10 (a), the PCS TFMGs may provide the fracture
resistance during deformation. At β~2, a small number of shear bands are found in some of
the marks, as indicated in Figure 4-10 (b). The formation of shear band indicates the PCS
TFMGs deform with an inhomogeneous plasticity.
The formation of shear bands in the microhardness marks increases with increasing β
ratio. In the case, propagation zone with shear bands at β~2.5 can be easily observed. The
propagation zone of shear band is along the directions out of the mark, as shown in Figure
4-11. At this stage, there is still no crack observed in all the marks. At β~3.5, the shear bands
can be observed even more easily in most marks, as shown in Figure 4-12. When β~5, shear
bands are observed obviously as shown in Figure 4-13. The spaces between shear bands
become much closer, and the widths of shear bands become finer. Figure 4-14 (a) shows the
enlarged image taken from Figure 4-13, indicating the small crack caused by particles. In
Figure 4-14 (a), it shows that the particles with size of ~1 µm will block the propagation of
shear bands. Since the shear bands are hindered, the stress released by propagation will
concentrate around the particles. Once the concentrated stress is over a critical value for the
PCS TFMGs, the cracks will be induced. Several cracks are found, but the cracks are all
limited just around the particles. In Figure 4-14 (b), the enlarged view exhibits the finer shear
bands.
For PCS-1000, β~3, shear bands are observed spreading over the entire area in the most
SEM images, as shown in Figure 4-15. There is no crack observed in all SEI images. When
β~5, some cracks are found in the mark, as shown in Figure 4-16. The morphology and the
position of crack are quite similar to that of the PCS-2000 at β~5. The above two results are
consistent with the dependence of hardness as a function of β in Figure 4-8. The similar
morphology and the same deformation mechanism further prove the hypothesis, i.e. the ratio
of β is a key point to determine the hardness of the system instead of only film thickness.
In some cases for PCS-1000, at β~8, the crack is not only formed around the particles,
but also starts to propagate along the shear bands, as shown in Figure 4-17. However, most of
the images show no crack, or cracks just around the particles. It means that the PCS-1000 can
still resist the load of 50 g. When β~11, the cracks can be observed easily as shown in Figure
4-18 (a). Based on all the images with cracks, it is deduced that when the load increases to a
critical level, the particles will play an important role in the deformation of the PCSTFMGs.
If there are not many particles with size of ~1 µm, crack will disappear in the marks, as
shown in Figure 4-18 (b). This result suggests that the particles with size of ~1 µm will result
in the crack propagation with increasing loads if many particles in such size are there. Once
the crack propagation becomes the dominant role, the film will peel off easily. For the
samples applied at a larger load, surface condition will dominate the deformation morphology
of samples.
The indentation depths for PCS-1000 and PCS-2000 are over the film thickness in
microhardness test, i.e. β >1 in all cases. The formation of shear bands increase with
increasing loads. Most of the films show no crack but shear bands. It can be concluded that
the shear bands formed in metallic glasses provide a moderate deformation. The PCS TFMGs
deposited on AZ31 can enhance the hardness, and the mechanism of shear bands prevents the
film from cracking, at least in the range of β < 5.
The nanoindentation mark of PCS-2000, β~2, is shown in Figure 4-19. The size is about
to that of PCS-2000 at β~2.5 in microhardness test. In Figure 4-19, it is found that the
nanoindentation mark is very clear, and no crack is observed in the mark. Some shear bands
appear just at the left side of the mark. In fact, shear bands can be observed at all the sides of
the mark, emerging inside and outside the mark, as indicated in Figure 4-20 (a) and Figure
4-20 (b).
The nanoindentation mark of PCS-1000 is shown in Figure 4-21. The size is a little
smaller than that of PCS-2000. It is coherent to the result in Figure 4-18. The morphologies
of PCS-1000 and PCS-2000 are quite similar after deformation. Although there are some
scratches in the surface of PCS-1000, the PCSTFMGs provide the fracture resistance with
shear bands during deformation. It can be concluded that the shear bands formed in metallic
glasses provide a moderate deformation both in microhardness and nanoindentation test.
4-4
Hardness calculation and comparison
In previous studies, various ceramic or metallic hard thin coatings have been applied for
preventing damage and improving the hardness properties of substrate [72,73]. For analyzing
the enhancement of hardness, the interaction between the hard thin coating and soft substrate
needs to be clarified under the different conditions. In 2001, a work-of-indentation approach
was extended to a general formula by Tuck et al. [74]. The hardness of each constituent
andcoating thickness can be integrated and expressed by
X s f
s k
H H H
H + β
+ −
= 1 (4-3)
Here H is the measured hardness reading, Hs is the relative minimal hardness of the substrate
with the hard coating thin film at β~ 10, Hf is the intrinsic hardness for the coated film, k is a
dimensionless hardness transition parameter, and X is the power exponent depending on the
deformation mode and geometry. With the above measured system hardness H, it is intended
to extract the relative substrate and film hardness based on equation 4-3. Since there are more
than one variables involved, we need to use the iterative extrapolation method to calculate the
best fit values of Hs and Hf, etc. The details of all fitting results for various samples are
presented in Table 4-2. Figure 4-22 shows the combined data from the least square curve fits
to the empirical data on the PCS coatings of 200, 500, 1000, and 2000 nm in thickness,
respectively, with the correlation coefficient R2between the model and experimental data
over 0.997. The model fitting is found well in accordance with the experimental data. The
measured datum points are marked with symbols and the model fit is shown by different lines.
Note that the experimental data used to fit in Figure 4-22 exclude those in the very shallow
regime with β less than 0.1, for the sake that these date show greater scattering. If only the
average hardness readings are included, the fitting is still good. The fittings indicate that the
Hs values for AZ31 substrate are located within 0.69 and 1.12 GPa, Hfvalues are within 6.59
to 7.98 GPa, k values within 7.08 and 22.03, and X values within 1.76 and 2.26.
For hardness values, it is expected that, as the thickness of the similar coatings increases,
and hence the coating plays a more important role in the energy absorption during indentation,
the hardness is expected to increase [74,75]. For the current experiment, the coatings of
different thicknesses possess similar microstructures, due to the same deposition conditions.
Therefore, the variations of X, k, Hs, Hf, and the measured apparent hardness H can be
discussed below.
The X value represents a hardness shifting factor between the substrate and coating film
with the different deformation modes, geometry, and interaction with each other. When the
thin film and the substrate material are both easier to deform together at the same time (as the
case of the 200 nm coating), the external pressures (indentation) can be more evenly
distributed the force to the film and substrate, resulting in a smaller X value and a smoother
hardness-β curve (Figure 4-22). On the other hand, as the coating is thicker over the critical
thickness (as the case of the 2000 nm coating), the coated film would become an independent
hard material with weaker interaction with the substrate as a separate bulk. Under applied
pressure or load, the film takes most of the deformation energy by itself as a victim material.
The resulting X value will be higher and the hardness-β curve will be steeper (Figure 4-22).
When the fatal force cannot be afforded by the coated hard thin film, the film will be
damaged or collapsed and the substrate will be exposed.
The above arguments may also be applied to the fitting parameter k value. The k value is
dimensionless hardness transition parameter that will affect the second term in equation 4-3,
namely, ∆H/(1+kβX), where ∆H represents (Hf – Hs). When k is small (as k=7.08 for the
thinner PCS-200 sample), the second term will be larger, leading to a higher measured
apparent hardness H, and vice versa. Meanwhile, the k value will also affect the relative
contribution of the load carrying by the substrate and film. Based on the calculation in ref.
[74], the hardness-β curves under a given X will shift to the right with increasing k value,
meaning the film will carry a higher percentage of indented load, and the high to low
hardness transition (or the deflection point in Figure 4-22) will sustain until a higher β ratio.
However, this trend is not so obvious since the X value is not fixed in Figure 4-22.
As for the extracted Hs and Hf, it can be seen from Table 4-2 that, with increasing film
thickness, the interaction between substrate and film becomes weaker, so that the relative
minimal substrate hardness Hs gradually decreases from 1.1 GPa to 0.69 GPa, and approaches
to the original AZ31 substrate hardness without coating (~0.52 GPa). Note that the extracted
Hs from the does not appear to be a fixed value ~0.52 GPa from the iterative extrapolation
method. This is mainly a result of the mutual interaction between the coated film and the
substrate, partly due to the residual stress retained in the soft AZ31 substrate and partly due to
the constraint from the film. At the same time, with increasing film thickness, the film
hardness gradually increases from 6.59 GPa to 7.98 GPa, and approaches to the ideal PCS
film material hardness (~8-10 GPa). This result is consistent with the previous finding [16]
that the intrinsic coated film hardness (Hf) would increase with increasing coated film
thickness.
From the experimental measured apparent hardness H, and the extracted film hardness
Hf, the 2000 nm sample always exhibits the much higher readings. This might give an idea
that the 2000 nm film coating would yield the best surface hardening effect for the AZ31 Mg
alloy. Nevertheless, the higher k and X values of this sample reveal the weaker interaction
between substrate and film, and the thicker film will carry most load and become prone to
film cracking problem. For solid bonding and better plasticity of the coated film, a lower X
and more even distribution of the applied load on both substrate and film would be a more
promising selection. With this consideration, the 200 nm coatings appear to be more feasible.
Finally, it is interesting to identify the range for the optimum PCS coated film thickness.
In this study, the PCS TFMG films thinner than 100 nm or less would lead to unsatisfactory
film coverage. The ultra thin film would often cause inadequate surface hardness. The
optimum extracted substrate relative hardness Hs is found to be around 200 nm. The predicted
trend of the relative substrate hardness as a function of the surface hard coating thickness for
the Pd77Cu6Si17 TFMGs deposited on the AZ31 substrate is presented in Figure 4-23. An
optimum hard coating will be highly useful for industry applications.