J Mater Sci (2013) 48:8052–8059
DOI 10.1007/s10853-013-7619-8
Copper-oxide whisker growth on tin–copper alloy coatings caused
by the corrosion of Cu6Sn5 intermetallics
Barbara Horváth • Balázs Illés • Tadashi Shinohara
Gábor Harsányi
•
Received: 25 April 2013 / Accepted: 22 July 2013 / Published online: 1 August 2013
Ó Springer Science+Business Media New York 2013
Abstract This paper reports the effect of corrosion
caused by high temperature and humidity on pure tin and
tin–copper alloy coatings. A new phenomenon was
observed; the development of copper-oxide whiskers on
tin–copper alloys plated on copper substrates (1–5 %
copper content stored at 105 °C/100 % relative humidity).
The copper-oxide whiskers showed similar growth properties to tin whiskers. We have made a model to understand
the development of copper-oxide whiskers. Localized
corrosion of the tin coating reaches the Cu6Sn5 intermetallic layer, and copper oxide accumulates after the corrosion of Cu6Sn5. The dilating SnOx compresses and extrudes
out the copper oxide in a whisker form.
Introduction
The formation of tin whiskers is a well-known reliability
issue in electronics: conductive monocrystalline tin whiskers grow spontaneously from the surface finish of the
component leads and can cause current leakage or short
circuits [1]. Tin whisker growth is caused by the development of compressive mechanical stresses in the tin surface finish, which can originate from residual stresses
caused by electroplating; stresses caused by the diffusion
of different metals during the intermetallic layer formation
B. Horváth (&) T. Shinohara
National Institute for Materials Science, 1-2-1 Sengen, Tsukuba,
Ibaraki 305-0047, Japan
e-mail: bhorvath@ett.bme.hu
B. Horváth B. Illés G. Harsányi
Department of Electronics Technology, Budapest University of
Technology and Economics, Egry József St. 18, Budapest 1111,
Hungary
123
[2, 3] or the growth of oxide in the tin layer; and thermally
or mechanically induced stresses [4]. In the presence of
compressive stress, the whiskers grow out as a stress
release mechanism [5, 6]. There has been some research on
the whiskering effects of copper in tin–copper alloy
platings [7–10], which is a widely used surface finish on
the electronic component leads, but these studies examined
only alloys with a smaller percentage of copper (up to
3.7 % Cu) on mainly electroplated coatings. In addition,
the ageing of the coatings has not been tested in highly
corrosive conditions; hence, the effects of oxidation on the
alloys have not been tested.
The appearance of oxides and the corrosion of the layer
may also cause the growth of whiskers. Several researches
have shown that the whisker growth at elevated temperature and humidity conditions can clearly be induced by the
oxidation or corrosion of the tin finish [11–13]. Oberndorff
et al. [14] tested matte tin plated leadframe packages in
high humidity that induced severe oxidation and corrosion
and observed a high molar volume of tin oxide which
resulted in whisker growth. Su et al. [15] created a statistical study of the whisker population and growth, where
they have stated that between the 60 °C/85 % RH and
60 °C/93 % RH conditions, the latter had a higher whisker
population per component and a longer maximum whisker
length, due to corrosion developed stresses. Osenbach et al.
[16] studied tin plated samples tested in similar conditions
and found that on regions of the tin layer where water
condensation was present, the entire thickness of the layer
has corroded and the corrosion product was highly crystalline SnO2.
Spontaneous development of copper-oxide whiskers on
tin coatings is a phenomenon which has not been observed
before. In our experiments, copper-oxide growth has been
studied with the similar stress-induced method as the
J Mater Sci (2013) 48:8052–8059
8053
growth of tin whiskers. But in this case, the development of
copper oxide is due to the galvanic corrosion of the layer
generated by the high temperature and humidity
circumstance.
Materials and methods
Six types of alloys were applied for the tests: 100 wt% Sn
(100Sn), 99 wt% Sn–1 wt% Cu (99Sn1Cu), 98 wt% Sn–
2 wt% Cu (98Sn2Cu), 97 wt% Sn–3 wt% Cu (97Sn3Cu),
96 wt% Sn–4 wt% Cu (96Sn4Cu) and 95 wt% Sn–5 wt%
Cu (95Sn5Cu) on copper base material. The surface finishes were created by using a dipping method, applying
450 °C pot temperature in all cases (in order to avoid the
copper crystal formation at lower temperatures). In inert
atmosphere (N2), 1-mm thick copper wires were dipped
firstly in H3PO4 (used as flux to remove surface oxides),
then into the molten alloys (or pure tin) about 1.5 cm deep.
The thicknesses of the developed surface finishes were
between 4 and 6 lm, and all samples were checked before
testing by polishing the cross-sections. The samples were
kept in highly corrosive environment [105 °C/100 % relative humidity (RH)] for up to 2400 h. Observations were
made by using scanning electron microscopy (SEM) in
every 200 h until the 1200th hour, then in every 400 h
thereafter. The cross-sections of the layers and whiskers
were created by focused ion beam (FIB), and were
observed by transmission electron microscope (TEM)
afterwards. The identification of the layer elements and
intermetallic types was carried out with energy-dispersive
X-ray spectroscopy (EDX) on both the SEM and later the
TEM samples; and the identification of copper oxides were
carried out with electron energy loss spectroscopy (EELS)
on the TEM samples.
Results
In this study, a very unique phenomenon was observed. In
the case of alloys with copper content, the material of the
developed whiskers was copper oxide. This phenomenon
occurred only on the surface of the Sn–Cu alloys, no
copper-oxide whiskers appeared on the pure tin plated
samples. The whiskering started after 600 h on the samples
(except 95Sn5Cu after 800 h). Higher copper content of the
alloys caused higher whisker densities; during the test very
dense (90–150 pieces/2500 lm2) but very short whiskers
(between 1.5 and 4.7 lm) developed (Fig. 1).
The two main influencing factors of the copper-oxide
whisker growth were the oxidation and the copper content
of the alloys. After 1200 h, it could be even visually seen
that the surface of the samples became heavily oxidized
Fig. 1 a Whiskers at the corrosion areas on the 96Sn4Cu sample,
105 °C/100 % RH, 1200 h. b EDX element mapping of whiskers.
The morphology of the copper-oxide whiskers in the image is
identical to tin whiskers
and that severe localized corrosion occurred on the samples
where water had condensed. A tin-oxide layer is evenly
found everywhere on the surface of the samples; however,
surface corrosion creates some localized thicker areas of tin
oxide that may span from the surface of the deposit down
to the substrate. Development of Cu oxide whiskers was
only found in these highly corroded areas, the rest of the
surface stayed intact (Fig. 1). At these areas where the Cu
oxide whiskers grow, there is no pure Sn layer left (see in
the ‘‘Discussion’’ section), so no chance for Sn whiskers to
develop.
The cross-section of a whisker and the layer underneath
observed by TEM–EDX analyses can be seen in Fig. 2.
The content of the whisker (M3–M5 in Table 1) shows that
the material of the emerging whisker is copper with a large
amount of oxygen. The increased ratio of the copper
indicates that there are additional copper spots inside the
CuxO matrix. Analysing the whiskers with EELS measures
the critical ionization energy EC that is sensitive to the
chemical situation of the material. Comparing the L23
edges and EC values with the references measured by
[17, 18] shows that the whiskers are built up by a mixture of
pure Cu and Cu2O (Fig. 3). The atomic percentage of oxygen is generally between 25 and 30, which means that the
ratio of Cu2O and Cu is 1Cu2O to 1Cu in case of 25 at.% O
and 3Cu2O to1Cu in case of 30 at.% O.
At the same time, a thin SnOx layer can be found on the tip
of the whisker and on the surface next to it (M1, M2) which
shows that the whisker broke through the layer, leaving some
SnOx on the tip. The area where the breakthrough of the SnOx
123
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J Mater Sci (2013) 48:8052–8059
whiskers
• M1
• M3
• M4
• M2
• SnOx
• M5
• Cu & Cu2O
enrichement
• M6
• SnOx & Cu2O
mixture layer
• Blocked
Cu2O
• M9
(a)
• Cu base
(b)
1 µm
• SnOx
• Cu3Sn
• M8
• M7
Breaking Area
BF
1 µm
Fig. 2 a TEM image of a Cu2O whisker on the 96Sn4Cu samples
after 2400 h (EDX results at the measurement points M1–M9 can be
seen in Table 1); b element mapping of Cu at the investigated area;
(c)
Cu K
1 µm
Sn L
c element mapping of Sn at the investigated area. The arrow indicates
the growing direction of the whisker
Table 1 Results of the EDX analysis of the Cu whisker area
O (at.%)
Cu (at.%)
Sn (at.%)
M1
72.27
6.39
21.34
M2
48.82
3.87
47.32
M3
M4
22.91
25.91
77.09
73.92
0.00
0.17
M5
22.54
77.04
0.42
M6
72.68
2.66
24.66
M7
75.28
3.42
21.30
M8
5.67
68.84
25.49
M9
45.10
22.82
32.08
layer had occurred is also marked in Fig. 2. Underneath the
whiskers (M6–M9), there is a SnOx-rich area with a small
amount of additional Cu. No Cu6Sn5 intermetallic layer can
be found anymore within the localized corrosion area,
although traces of Cu3Sn can be found on some relatively
small parts of the inner layer (M8).
In most cases inside the SnOx area, vertical lines can be
observed heading towards the surface where Cu traces can
be found (Fig. 4). These lines are also slightly visible in
Fig. 2. It is assumed that the SnOx is the original corroded
coating or had been formed by the separation from the
Cu6Sn5 by corrosion, while CuxO has been penetrated
through these vertical lines towards the surface and then
appearing as whiskers. An interesting phenomenon can
also be seen in Fig. 2: the remaining Cu3Sn layer can block
the Cu2O penetration towards the surface, when Cu particles are trapped underneath it.
No copper-oxide whiskers have developed on the samples with 100 % Sn coating, although several corroded
areas can be found similar to the alloyed coatings. In Fig. 5,
the TEM image and the EDX analyses of the cross-section
123
Fig. 3 EELS spectrum measured in a whisker. The background was
subtracted from the spectrum and the intensities normalized to the
same value
of a corroded area can be seen in such sample types. The
results show that the separation occurred within the layer in
the corroded areas similar to the Sn–Cu alloys; in some
areas, CuxO had developed within the coating while in other
areas enrichment of SnOx occurred. No Cu6Sn5 intermetallic layer can be found and high amount of oxygen atoms
can be found all across the layer until the Cu substrate.
Additionally, no vertical lines with Cu traces are observed,
which can been seen in Fig. 4.
Figure 6 shows the TEM image and EDX analysis of an
area where localized corrosion did not occur. It can be seen
that the structure of the layers follow the usual intermetallic appearance; underneath the Sn layer Cu6Sn5 and
J Mater Sci (2013) 48:8052–8059
Cu2O & Cu
enrichment
8055
and form intermetallic compounds at the interface. The
diffusion is faster at elevated temperature and storing the
samples at 105 °C for 2400 h generates a large mass of
Cu6Sn5 intermetallic within the tin coating, consuming the
majority of the layer itself. The thickness of the developed
intermetallic layer is around 1–2 lm.
Localized corrosion develops on the surface of the
coating when water vapour condenses from the air as
micro-water droplets, and corrosive O2 is absorbed at
these surfaces. Most metal corrosion occurs via electrochemical reactions at the interface between the metal
and an electrolyte. Electrochemical corrosion involves
two half-cell reactions: an oxidation reaction at the
anodic site and a reduction reaction at the cathodic site
[19]. For tin corroding in water with a near neutral pH,
these half-cell reactions can be represented as an anode
reaction:
SnOx & Cu2O
mixture layer
Cu2O & Cu
pentration lines
• Cu3Sn
Cu substrate
Sn ! Sn4þ þ 4e
1 µm
ð1Þ
BF
and cathode reaction:
Fig. 4 TEM image of the layer under a Cu2O whisker containing a
mixture of SnOx and Cu2O on the 95Sn5Cu samples after 2400 h. The
visible remaining lines of Cu2O and Cu penetrating towards the
surface can be observed
Cu3Sn layers can be found. No oxygen can be found within
the layer and no separation of the intermetallic layer and
accumulation of copper oxide is observed.
O2 þ 2H2 O þ 4e ! 4OH
ð2Þ
Within the droplet, the hydroxide ions can move inward
to react with the tin(II) ions moving from the oxidation
region, thus tin(II) hydroxide precipitates. Corrosion
products are then quickly produced by the dehydration of
the precipitate. This can be represented by the following
equation:
Sn4þ þ 4OH ! SnðOHÞ4
ð3Þ
Discussion
SnðOHÞ4 ! SnO2 þ 2H2 O
ð4Þ
According to our hypothesis, the previously experienced
results developed with the following model, explained in
this section. Instantly after creating the coating, the copper
atoms from the substrate diffuse into the deposited tin layer
While the localized corrosion areas on all the copper
alloy coatings were dense with copper whiskers, the
corrosion areas on the pure tin coated samples contained
only SnOx corrosion product.
(a)
Cu
(b)
MP O Sn
(c)
Cu
enrichment
SnOx & Cu2O
mixture layer
0%
50%
1 µm
100%
BF
Cu base
1 µm
Cu K
1 µm
Sn L
Fig. 5 a TEM image and EDX analyses of a corroded area on the 100Sn sample with element distribution on different measuring points (MP),
b element mapping of Cu and c element mapping of Sn
123
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J Mater Sci (2013) 48:8052–8059
(a) 0%
50%
100%
(b)
(c)
Sn
Cu6Sn5
Cu6Sn5
• Cu3Sn
• Cu3Sn
Sn O
MP
1 µm
Cu
BF
Cu base
1 µm
Cu K
1 µm
Sn L
Fig. 6 a TEM image and EDX analysis of a non-corroded area on the 100Sn sample with element distribution on different MP, b element
mapping of Cu and c element mapping of Sn
SnOx develops during the corrosion of pure tin coatings,
while spots of CuxO will also develop within the SnOx for
Sn–Cu coatings, since corrosion also occurs on the copper
clusters in the Sn–Cu alloy. The copper will be oxidized by
the dissolved oxygen in the water forming copper(I) oxide
(Cu2O) with the following reaction:
4Cu þ O2 ! 2Cu2 O
ð5Þ
Cu can form two stable oxide phases, Cu2O and CuO,
under oxidizing conditions. It was found that CuO is
formed mainly from chemically cleaned Cu [20] and in dry
condition [21], while in the presence of water with
corrosion effect—such as in our test condition—the
formation of Cu2O is more likely [20].
During the localized corrosion of the tin (and tin–copper
alloy) coating, water and oxygen easily reach to the Cu6Sn5
intermetallic. Tin is anodic to copper and copper alloys and
to the intermetallic compounds formed between tin and
copper in most aqueous environments, and hence, the
corrosion of the coating accelerates inwards in the layer
[22]. Because the developed SnOx (and traces of CuxO)
corrosion products are precipitated as a result of secondary
reactions, it is porous and absorbent which encourages
further corrosion. Hence, inward water diffusion may
penetrate into it [23] and cause further corrosion in the
intermetallic layer (by this time, intermetallic growth has
already saturated).
It is obvious that the copper content of the alloys is
too low by itself to form the experienced amount of
copper-oxide whiskers, so the copper must originate
from the substrate; which is mostly available from the
intermetallic region. Most intermetallic compounds have
either only good mechanical or environmental properties. Materials with excellent resistance against oxidation and hot corrosion have relatively low strength,
123
while higher specific strength modulus alloys have
poorer oxidation resistance [24]. While the Cu3Sn phase
is significantly more stable and less prone to corrosion
attack than the Cu6Sn5 phase, it has been determined
that the corrosion behaviour of Cu6Sn5 is almost as
corrosive as pure Cu [25]. Investigations with dental
amalgams [26, 27] show that the most corrosion prone
phase in high copper amalgams is the Cu6Sn5 phase
where corrosion processes lead to the release of SnOx.
Due to the meeting of the water with the intermetallic,
Cu6Sn5 converts to Sn(OH)2 and Cu(OH)2 which
instantly oxidize and transform into SnO2 and Cu2O,
respectively. For breaking up the Cu6Sn5 intermetallic,
the ionic reaction equation with concerning the corrosion product is the following:
Cu6 Sn5 þ 13OH ! 5SnO2 þ 3Cu2 O þ 13Hþ þ 26e
ð6Þ
Hence, the total equation of the reaction for breaking
up the Cu6Sn5 intermetallic can be given at 105 °C
temperature as:
Cu6 Sn5 þ
13
O2 ! 5SnO2 þ 3Cu2 O
2
ð7Þ
Calculate the change in enthalpy of reaction Eq. (7)
assuming standard condition:
X
X
mi Df Hi0ðproductsÞ mj Df Hj0ðreactantsÞ ¼
Dr H 0 ¼
i
j
0
0
0
¼ 5Df HðSnO
þ 3Df HðCu
Df HðCu
2Þ
2 OÞ
6 Sn5 Þ
¼ 3376:07 kJ/mol
13
0
Df HðO
2Þ
2
ð8Þ
where m is the stoichiometric number of each reactants and
products. Calculate the change in entropy of reaction
Eq. (7) assuming standard condition:
J Mater Sci (2013) 48:8052–8059
Dr S0 ¼
X
mi S0iðproductsÞ X
i
¼
5S0ðSnO2 Þ
8057
mj S0jðreactantsÞ
j
þ
3S0ðCu2 OÞ
S0ðCu6 Sn5 Þ ¼ 0:7069 kJ/mol:K
13 0
S
2 ðO2 Þ
ð9Þ
The enthalpy and entropy changes for SnO2, Cu2O, O2,
Cu and Cu6Sn5 are expressed in Table 2. The standard
Gibbs free energy change of reaction (DrG0) for Eq. (7) is
determined as:
Dr G0 ¼ Dr H 0 TDr S0 ¼ 3108:86 kJ
ð10Þ
According to Eqs. (8), (9) and (10), the forward direction of reaction Eq. (7) is thermodynamically possible.
Thus, the reverse reaction is impossible at 105 °C which
implies that the developed SnOx corrosion product cannot
pass their oxygen atoms to the neighbouring Cu6Sn5 layer.
When the water and oxygen reach to the Cu6Sn5 intermetallic, oxygen diffuses into the Cu6Sn5 layer, breaks up
the intermetallic material, creates more SnOx and enrichment of Cu2O occurs [31, 32]. Although Cu2O is a porous
material, oxygen transport within the inner layers cannot go
perfectly across the structure of the Cu2O. Instead, the
developed Cu2O breaks up the neighbouring Cu6Sn5 in
parts that was originally further away from the main oxygen source. This can be expressed by the following
equation:
10Cu2 O þ Cu6 Sn5 ! 26Cu þ 5SnO2
ð11Þ
Calculating the standard Gibbs free energy change of
reaction Eq. (11) (similarly as for Eqs. 8, 9 and 10), it
results in DrG0 = -1241.89 kJ/mol which means that the
forward direction of this reaction is also thermodynamically
possible. Since the O and Sn atoms diffuse into SnO2 in the
area, the developed Cu stays unreacted around the Cu2O
area, creating a mixture of Cu2O ? Cu within the layer.
During the Cu6Sn5 intermetallic layer growth, the diffusing atoms form intermetallic compounds within the Sn
grain boundaries. In this case, volume expansion occurs by
the dominant diffusion of Cu into Sn which results in the
Table 2 Enthalpy and entropy changes for different elements and
compounds at 400 K
Component
DfH0 Enthalpy
(kJ/mol)
S0 Entropy
(J/mol K)
SnO2
-574.38
69.29
[28]
Cu2O
-170.64
111.53
[29]
Cu6Sn5a
-7.75
0.37
Reference
[30]a
O2
0
213.87
[29]
Cu
0
40.48
[29]
a
Enthalpy and entropy changes at 298 K, no values can be found in
literature for 400 K
volume expansion in the coating. The molar volume of the
original Sn layer is replaced with that of Cu6Sn5 intermetallic, where the former is smaller than the latter, causing a
compressive force resulting from the volume expansion
[33]. Compressive stress is necessary in the Cu2O ? Cu
area for the initiation and growth of copper-oxide whiskers.
When SnOx is transformed continuously from the Cu6Sn5
layer, the volume of the corroded area expands because
SnOx and Cu2O are significantly lower in density than
Cu6Sn5. The density of Cu6Sn5, Cu2O and SnO2 is 8.3, 6.0
and 6.95 g/cm3, respectively.
Hence, a compressive stress is generated by the corrosion of the tin that can drive the nucleation and growth of
copper-oxide whiskers by a mechanical extruding process.
Weak spots on the oxide layer are necessary for the surface
oxide to break when Cu2O ? Cu is pushed towards the
surface. This can relieve the developed internal compressive stress, and hence whisker formations can grow [34].
The oxide layer within the Sn–Cu alloy coatings already
has spots of Cu2O clusters from the initial corrosion of the
coating surface. The hardness of the tin oxide is considerably larger than the hardness of the copper oxide (Mohr
hardness of SnO2 is 6.5 and Mohr hardness of Cu2O is
3.5–4). Therefore, the copper oxide can break through and
grow out on the weakened areas of the corroded layer and
exists in a whisker form (Fig. 7) on the samples with Sn–
Cu alloy coatings. As it can be seen in Fig. 2, a layer of
SnOx remain can be found on the tip of the whisker.
One possible explanation for why no copper-oxide
whiskers developed on the samples coated with pure Sn is
because the copper oxide could not break through the
continuously hard tin-oxide layer, since no Cu2O clusters
developed in the coatings of the samples in early stage. The
previously introduced hypothesis was proven by TEM
measurements of the layer structure. By observing the
TEM measurements of the pure tin samples (100Sn) in
Fig. 5, it can be shown that the copper oxide (Cu2O)
develops within the layer instantly by the break-up of the
Cu6Sn5 intermetallic, and not by developing Cu independently by selective corrosion of the Sn, and oxidizing it by
humidity after it extrudes out of the surface as a whisker.
Though copper-oxide whiskers could be considered as a
reliability issue, Cu2O nanostructures have a useful side as
well. Cu2O is a p-type semiconductor with a direct band
gap of 2.17 eV, and is a promising material with a potential
application in lithium-ion batteries, catalysis, solar energy
conversion and magnetic storage devices [35, 36]. Compared with traditional semiconductor materials, copper
oxide is cheaper, has low toxicity and possesses good
environmental properties. Various Cu2O and CuO microand nanostructures have been developed by synthesization
[37], oxidizing Cu nanowires [38, 39] or by high-yield
thermal annealing [40]. Understanding the phenomenon
123
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J Mater Sci (2013) 48:8052–8059
(a)
(b)
Rest of the
SnCu layer
Localized
Corrosion
CuxO
SnOx
SnOx
Cu2O & Cu
enrichment
Cu2O whisker
Localized
corrosion
SnOx
SnOx
O2
Cu6Sn5
SnOx
Cu3Sn
SnOx Cu2O
Cu
Cu substrate
Cu3Sn
Cu2O
Cu6Sn5
Cu substrate
Blocked
Cu2O
Penetration
lines
Fig. 7 The mechanism of copper-oxide whisker growth: a the tinoxide layer develops with CuxO spots within, while at the same time
Cu6Sn5 intermetallic layer grows rapidly. b after the corrosion of
Cu6Sn5, copper oxide is piling-up. The dilating SnOx compresses the
copper oxide causing it to extrude at the weakened areas of the
surface oxide
detailed in this paper could result in building Cu2O whisker
structures induced by stress within the coating. Controlled
development of Cu2O can be obtained by breaking down
Cu6Sn5, and systematically placing Cu nanoparticles
within the Sn coating. Based on the results of this research,
a new method of creating different structures of cuprous
oxide nanowires can be developed in the future.
References
Conclusion
Copper-oxide whisker growth has been observed on tin–
copper alloy platings (1–5 % copper content) on copper
substrate when exposed to corrosive high temperature and
humidity circumstances (105 °C/100 % RH). The growth
behaviour of the copper-oxide whisker is hypothesised to
be due to the following. Localized corrosion occurs on the
samples where water had condensed causing the tin alloy
coating to convert to SnOx with CuxO clusters within.
Meanwhile, 1–2 lm of Cu6Sn5 intermetallic layer grows
between the alloy coating and the copper substrate. When
water and oxygen reach to the Cu6Sn5 intermetallic,
Cu6Sn5 corrodes and enrichment of copper oxide occurs.
Since the SnOx is dilating, it is compressing the copper
oxide; therefore, it breaks out at the weakened areas of the
surface oxide in a whisker shape. Copper-oxide whiskers
did not develop on the samples coated with pure tin
because the accumulated copper oxide cannot break
through the continuous hard SnOx layer, where no CuxO
had developed in the coatings near the surface.
Acknowledgements The authors would like to thank Prof. Masahiro Seo personally for the discussions about the theories of this work.
The work reported in the paper has been developed in the framework
of the project ‘‘Talent care and cultivation in the scientific workshops
of BME’’ project. This project is supported by the grant TÁMOP—
4.2.2.B-10/1–2010-0009. This work has been carried out through the
Joint Graduate School Program between the Budapest University of
Technology and Economics and the National Institute for Materials
Science, Japan.
123
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