Microscopy: advances in scientific research and education (A. Méndez-Vilas, Ed.)
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Observation of thermal roughening transition in nickel surface dissolved
by an electrochemical technique
M. Saitou
Department of Mechanical Systems Engineering, University of the Ryukyus 1 Senbaru, Nishihara, Okinawa, 903-0213,
Japan
A thermal roughening transition in a polycrystalline nickel surface dissolved anodically in a solution of sulfuric acid has
been investigated using a confocal laser scanning microscope. The research focus in our paper is twofold: (1) In current
pulse dissolution, a drastic change in surface roughness from a smooth surface to a rough surface is observed at a transition
temperature, at which a discontinuity appearing in a normalized dissolution mass occurs. Within the framework of the
Kosterlitz-Thouless transition, the smooth surface is thought to be formed by the motion of a kink-antikink pair, whereas
the rough surface is generated by the random formation of an adatom-vacancy pair. The transition temperature decreases
with the concentration of sulfuric acid. An equivalent electric circuit model that describes the electric double layer is
shown to well represent the frequency-dependence of the normalized dissolution mass. (2) In direct current dissolution, the
discontinuity in the normalized dissolution mass is not found, but a large change in the dissolution rate at a temperature is
found. The temperature is thought to be a one at which the dominant dissolution mode changes from the motion of the
kink-antikink pair to the random formation of the adatom-vacancy pair. We name the temperature as the mode change
temperature, which decreases with the concentration of sulfuric acid as well as the transition temperature.
Keywords: confocal laser scanning microscope; surface roughness transition; nickel; anodization; Kosterlitz-Thouless
transition
1. Introduction
A great number of investigations on a change in surface morphology etched [1,2] or deposited [3] by sputtering,
formed by thermal annealing [4-7], and etched by chemical dissolution [8, 9] have been carried out. A clean surface
undergoes the roughening transition at the temperature at which some defects are formed spontaneously [6]. The
thermal roughening proceeds by the Kosterlitz-Thouless (KT) transition [10-12] caused by the formation of defects
called a basic excitation, i.e., a kink-antikink pair and adatom-vacancy pair formation. For example, in a smooth surface
at an atomic level, the excitation is the formation of the adatom-vacancy pair. The surface roughness evolution in a thin
film, which relates to statistical surface growth models such as KPZ [13], has been discussed.
In the anodic dissolution of silicon, non-thermal roughening transition between a polishing and pore surface [14],
which was dependent on the current density, was analyzed with the statistical surface growth model. Charge transfer
reactions in an electrochemical dissolution process take place in an electric double layer [15] that exists between an
anode electrode and etching liquid. The function of the electric double layer is treated mainly as a capacitor [16]
dependent on the frequency of an applied current. The prediction of the equivalent electric circuit model, which is
considered to be a kind of mean-field theory, is found to well describe the frequency-dependence of electrodeposition
mass [17]. In this study, we will apply the equivalent electric circuit model so as to describe the frequency-dependence
of a normalized dissolution mass.
Current pulse dissolution has the advantage of three parameters varied independently [19], i.e., the current pulse
density, pulse on-time, and pulse off-time. In general, the current in current pulse dissolution consists of the Faradaic
current and non-Faradaic current. The Faradaic current contributes to electrodissolution described by a charge transfer
reaction, whereas the non-Faradaic current just only passes through the electric double layer. In this study, nickel
electrodissolution from a sulfuric acid solution was chosen to investigate the dissolved mass because it had a current
efficiency, higher than 98 % for a low current density in direct current electrodissolution [20].
For a low current density in direct current dissolution, a non-thermal roughening transition in the surface morphology
was found [21-22] on the basis of the statistical surface growth model. In this study, we focus on the thermal
roughening transition in a nickel surface for a high current density.
As the electric double layer has a property of a capacitor, the current pulse is a suitable choice for the investigation
on the frequency-dependent dissolution process. The measurement of dissolution mass that is a fundamental quantity
leads to the obvious change in the anodic dissolution mass at the transition temperature. The normalized dissolution
mass represented by the ratio between the actual dissolution mass and the dissolution mass expected from the Faraday's
law is employed to describe the thermal roughening transition.
In the present study, we will demonstrate the thermal roughening transition in the anodic dissolution of a
polycrystalline nickel surface in a solution of sulfuric acid. The drastic change in the surface morphology from the
smooth to the rough surface at the transition temperature is observed using a confocal laser scanning microscope.
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2. Experimental Setup
2.1
Current pulse dissolution
The experimental procedure was as follows: A polycrystalline nickel plate (purity 99.95 %) of 30x10 mm2 and a nickel
square plate of 80 mm were prepared for an anode and cathode electrode. The two electrodes cleaned by a wet process
were located parallel in an electrochemical cell containing sulfuric acid (mol/L) : 0.5, 1.0, and 2.0. Only one side of
10x10 mm2 in the anode electrode was dissolved by the rectangular current pulse because the other side of the anode
electrode was coated with an insulating organic thin film to prevent dissolution. The whole nickel plate for the cathode
electrode was immersed into the solution. The area of the cathode electrode was 128 times as large as that of the anode
electrode. Hence, when the electric double layer was expressed as electrical components [18], the resistance and
capacitance in series of the cathode electrode in the solution were ignored in comparison with those of the anode
electrode.
The electrochemical cell was maintained in a range of temperature from 293 K to 319 K. The rectangular current
pulse was supplied with a current pulse generator. The peak amplitude of the rectangular current pulse having a
frequency of 10 to 1000 Hz was 82 mA/cm2. The current on-time was chosen to be equal to the current off-time. Using
the rectangular current pulse parameters, the mass of nickel dissolved anodically in the sulfuric acid for 1604 s becomes
20 mg/cm2 when the current efficiency is 100 %. Here the current efficiency is defined as the ratio of the actual amount
of nickel dissolved into the solution to that expected from the Faraday's law.
After dissolution, the nickel anode electrode was weighed to a precision of 0.1 mg with an electric balance. The ratio
between the actual dissolved nickel mass, ma and the dissolved nickel mass, me expected for the 100 % current
efficiency from the Faraday's law was determined for a variety of frequency and temperature. We call the ratio me/ma as
the normalized dissolution mass. The etched surface of the anode electrode was observed and measured with a confocal
laser scanning microscope, which determined to an accuracy of 0.025 μm in depth and provided a digitized microscopic
image with a resolution of 780 x 564 pixels.
2.2 Direct current dissolution
A polycrystalline nickel plate (purity 99.95 %) of 30x5 mm2 and a nickel square plate of 80 mm were prepared for an
anode and cathode electrode. Only one side of 20x5 mm2 in the anode electrode was dissolved by the direct current. The
two electrodes cleaned by a wet process were located parallel in an electrochemical cell containing sulfuric acid
(mol/L): 0.5, 1.0, and 1.7. The whole nickel plate for the cathode electrode was immersed into the solution.
The electrochemical cell was maintained in a temperature range from 300 to 323 K. The direct current having a
range from 140 to 300 mA/cm2 was supplied by a direct current generator. The high current density was chosen because
little change in the normalized dissolution mass at a low current density, which was approximately equal to 1, was
caused by temperature and a concentration of sulfuric acid. After dissolution, the nickel anode electrode was weighed to
a precision of 0.1 mg with the electric balance.
3. Results and Discussion
3.1
Current pulse dissolution
The surface images of the nickel electrode dissolved anordically at 317 K and 318 K in the 0.5 mol/L sulfuric acid
solution, which were observed with the confocal laser scanning microscope, are shown in Fig. 1. In Fig. 1 (a), the
etched surface comprises grains with smooth surfaces and grain-boundaries that appear as meandering strings.
Fig. 1 Surface images of the nickel anode electrodes dissolved at a frequency of 500 Hz in the 0.5 mol/L
sulfuric acid solution. (a) A microscopic surface image of the nickel anode electrode at a dissolution temperature
of 317 K. (b) A microscopic surface image of the nickel anode electrode at a dissolution temperature of 318 K.
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The surface in Fig. 1 (a) has a mirror-like appearance. In contrast with Fig. 1 (a), figure 1 (b) shows that the surface
image of the nickel electrode dissolved at 318 K appears prominently rough. No grain-boundary and no smooth surface
are observed. The surface appearance has a semidull luster.
Fig. 2 Surface images of the nickel anode electrodes dissolved at a frequency of 500 Hz in the 1.0 mol/L sulfuric
acid solution. (a) A microscopic surface image of the nickel anode electrode at a dissolution temperature of 310 K. (b)
A microscopic surface image of the nickel anode electrode at a dissolution temperature of 311 K.
In Fig. 2, the surface images of the nickel anode electrode dissolved at 310 K and 311 K in the 1.0 mol/L sulfuric
acid solution are shown. The grain boundaries are clearly visible in Fig. 2 (a), however, the presence of the grain
boundaries is unapparent in Fig. 2 (b) as well as in Fig. 1 (b). The surface in Fig. 2 (a) has a mirror-like appearance
similar to the surface in Fig. 1 (a). The temperature at which the surface appearance changes from the smooth to the
rough surface decreases in comparison with the temperature in Fig. 1.
Fig. 3 Surface images of the nickel anode electrodes dissolved at a frequency of 500 Hz in the 2.0 mol/L sulfuric
acid solution. (a) A microscopic surface image of the nickel anode electrode at a dissolution temperature of 306 K.
(b) A microscopic surface image of the nickel anode electrode at a dissolution temperature of 307 K.
In Fig. 3, the surface images of the nickel electrode dissolved in the 2.0 mol/L sulfuric acid solution at 306 K and 307
K are shown. The grain boundaries are clearly visible in Fig. 3 (a), however, the presence of the grain boundaries is
unapparent in Fig. 3 (b) as well as in Figs. 1 (b) and 2 (b). The surface has a mirror-like appearance similar to the
surface in Figs. 1 (a) and 2 (a). The temperature at which the surface appearance changes from the smooth to the rough
surface becomes lower than that in the 1.0 mol/L sulfuric acid solution.
In Fig. 4, the surface roughness profiles measured with the confocal laser scanning microscope are shown. The
nickel electrodes were dissolved anordically at 1000 Hz. Figure 4 (a) shows smooth terraces and grain boundaries. In
Fig. 4 (b), the surface roughness of the terrace is small, whereas the grain boundary is as deep as a well because the
grain boundary has a higher dissolution rate than the terrace. According to the KT transition, the dissolution mechanism
that yields a smooth terrace in the grain is thought as follows: Atoms in the kink-antikink pair [12] dissolve into the
solution, and the kink-antikink move step by step [6]. The motion of the kink-antikink pair forms the smooth terrace. In
addition, the coalescence of the kink-antikink pair also yields the smooth surface.
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In contrast with Fig. 4 (a), figure 4 (c) shows that the surface image of the anode electrode dissolved at 1000 Hz
appears prominently rough as well as the surface image in Fig. 2 (b) dissolved at 500 Hz. No grain-boundary and no
terrace with a smooth surface are observed. Figure 4 (d) shows a great change in the surface roughness owing to the
random formation of the adatom-vacancy pair. The adatom, which in this study is a nickel atom in the anode electrode,
dissolves as a nickel ion in the solution. Within the framework of the KT transition, the formation of the adatomvacancy pair [11] that requires more bonds to be broken than the kink-antikink pair creation occurs at a higher
temperature. In addition, if the formation of the adatom-vacancy pair occurs randomly in an entire electrode surface, the
surface roughness increases with time. The smooth terrace is obtained below the thermal roughening transition
temperature, which may be used for mirror polishing in manufacturing.
Fig. 4 Surface images of the nickel anode electrodes dissolved at a frequency of 1000 Hz in the 0.5 mol/L sulfuric acid
solution and their surface height measured along a scanline (white line) with the confocal laser scanning microscope. (a) A
microscopic surface image of the nickel anode electrode at a dissolution temperature of 317 K. (b) A plot of the surface height
vs. distance measured along the white line in Fig. 4 (a). (c) A microscopic surface image of the nickel anode electrode at a
dissolution temperature of 318 K. (d) A plot of the surface height vs. distance measured along the white line in Fig. 4 (c).
Thus, the microscopic images make clear the presence of thermal roughening transition. So as to investigate a
dissolution mechanism in detail, the weight loss dissolved in the sulfuric acid solution while the current passes through
the anode and cathode electrode was measured using the electric balance.
In order to describe the frequency-dependence of the normalized dissolution mass, we apply an equivalent electric
circuit model for the electric double layer explained in detail elsewhere [21]. In Fig. 5, the electric circuit [16]
comprising the capacitance C, the inner electric resistance Rl, and the leakage resistance r represents the electric double
layer.
Fig. 5 Schematic diagram of the electric circuit model equivalent to
the elctric double layer. The electric double layer comprises the
leakage resistance r, the capacitance C, and the inner electric
resistance Rl. The elecrochemical dissolution process is represented
by the reaction resistance Rch.
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Microscopy: advances in scientific research and education (A. Méndez-Vilas, Ed.)
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The charge transfer reaction in the dissolution process ( Ni + OH − → Ni 2+ + OH − + 2e − ) has a potential barrier that
impedes dissolution, which means some energy required to proceed the reaction. Hence, it is thought to be appropriate
to express the charge transfer reaction as an electric resistance, which is called the reaction resistance, Rch. As the circuit
model in dissolution is equivalent to that in electrodeposition, we have the following equation [21] for the normalized
mass ma/me dissolved by the rectangular current pulse having the frequency f=1/2T where T is the current on-time (or
current off-time),
ma
=
me
1
R
1 + ch
r
 
Rl
1 + 1 −
  Rl + R c
 1 e −α T − 1

,
−α T
+ 1
α T e
(1)
where α = [C ( Rl + Rc )]−1 and R c = rR ch /( r + R ch ).
Figure 6 shows a plot of the normalized dissolution mass ma/me vs. the frequency of the rectangular current pulse for
four kinds of the solution temperature. In Fig. 6 (a) for a sulfuric acid solution of 1.0 mol/L, the values of ma/me at 300
K and 310 K exponentially decrease with the frequency and tend to approach a fixed value much less than 1.0. The
frequency-dependence of the dissolution mass is due to the capacitative property of the electric double layer represented
as the capacitor. Hence, the current that does not contribute to dissolution passes through the electric double layer. For f
>> α/2, Eq. (1) approaches a fixed value,
ma
1
=
me
 Rch
21 +
r


Rl
1 +
  Rl + Rc



.

(2)
On the other hand, the values of the normalized dissolution mass at 311K and 312 K in Fig. 6 (a) are independent of
frequency and approximately equal to 1.0. For Rch → 0, Eq. (1) intends to approach 1.0. Owing to the reaction
resistance Rch much less than the impedance of the capacitor C, most of the current is used for dissolution at the
temperature of 311 K and more. The difference in the saturated dissolution mass between 310 K and 311 K in Fig. 6 (a)
is obvious. As shown in Fig. 6 (b), the similar difference in the saturated dissolution mass at 306 K and 307 K is
obtained for the 2.0 mol/L sulfuric acid solution. The equivalent electric circuit model, which is considered to be a kind
of mean-field theory, cannot indicate the presence of transition temperature but well describes the frequencyindependence of the normalized dissolution mass under or above the transition temperature.
The solid line in Fig. 6 (a) shows the calculation result of Eq. (1) best fitted to ma/me at 310K using Rl=9 Ω, C=180
μF, Rch/r=1x10-2, and Rc=25 Ω. In a similar way, the solid line in Fig. 6 (b) is depicted using Rl=16. 5 Ω, C=180 μF,
Rch/r=1.5x10-2, and Rc=38.4 Ω. These values are the same in the order of magnitude as those used in previous studies
[18, 21]. As shown in Fig. 6, the frequency-dependence of the normalized dissolution mass ma/me obeys Eqs. (1) and
(2).
The double layer capacitance C and leakage resistance r remain fixed, which implies that the geometric dimension of
the electric double layer does not change in the range of the concentration of sulfuric acid. An increase in the sulfuric
acid concentration increases the inner resistance Rl and reaction resistance Rch. An increase in Rl increases the current
used for dissolution. On the other hand, an increase in Rch decreases the current used for dissolution. As a result, the
saturated ma/me almost keeps constant irrespective of the concentration of sulfuric acid.
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Fig. 6 Frequency-dependence of the normalized dissolution mass in the 1.0 and 2.0 mol/L sulfuric acid solution for four kinds of
temperature. The solid line shows Eq. (1) best fitted to the normalized dissolution mass ma/me : (a) at 310 K using Rl=9 Ω, C=180 μF,
Rch/r=1x10-2, and Rc=25 Ω for the 1.0 mol/L sulfuric acid solution, and (b) at 306 K using Rl=16.5 Ω, C=180 μF, Rch/r=1.5x10-2, and
Rc=38.4 Ω for the 2.0 mol/L sulfuric acid solution.
The equivalent electric circuit model predicts the dissolution that occurs like an avalanche owing to the zero reaction
resistance Rch=0. These interpretations well explain the normalized dissolution mass approximately equal to 1.0 in Fig
6.
The dissolution by the formation of the adatom-vacancy pair occurs in an entire electrode area at the transition
temperature, whereas the dissolution by a kink-antikink pair occurs in a local area near the kink-antikink pair. Hence, in
the equivalent electric circuit model, the average reaction resistance for the dissolution by the formation of kinkantikink pair remains finite because the dissolution by the kink-antikink pair does not occur outside of the kinkantikink pair. On the other hand, the average reaction resistance for the dissolution by the adatom-vacancy pair
formation becomes zero because the formation of the adatom-vacancy pair occurs everywhere in the anode electrode.
Figure 7 shows the dependence of the transition temperature on the concentration of sulfuric acid. The transition
temperature decreases with the concentration of sulfuric acid. Since the saturated ma/me at 306, 310, and 317 K
becomes 0.65, 0.64, and 0.65 respectively, the dissolution rate approximately has the same value. On the other hand, the
dissolution rate generally increases with the concentration of sulfuric acid and temperature. Hence, the higher
concentration of sulfuric acid yields the lower transition temperature.
Fig. 7 A plot of the transition temperature vs. the concentration of sulfuric acid.
3.2 Direct current dissolution
Figure 8 shows the temperature-dependence of nickel mass dissolved by a direct current density of 140, 250 and 300
mA/cm2. In Fig. 8 (a), the dissolution mass increases with the temperature and shows an abrupt change at a temperature
of 322.5 K. In Fig.8 (b), the dissolution mass also abruptly increases at a temperature of 322 K. However, no
discontinuity in the normalized dissolution mass obviously exists. This is different from a change in the normalized
© FORMATEX 2014
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Microscopy: advances in scientific research and education (A. Méndez-Vilas, Ed.)
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dissolution mass in Fig. 6. The two modes, the formation of the kink-antikink pair and that of the adatom-vacancy pair
will coexist in an experimental range of temperature and the dominant dissolution mode will change at the temperature
such as 322 K and 322.5 K. In fact, even at a high current density of 300 mA/cm2, the normalized dissolution mass
moderately increases at a temperature of 322 K in Fig. 8 (c) in comparison with that at the current density of 140 and
150 mA/cm2.
Fig. 8 A plot of the normalized dissolution mass vs. temperature for the 0.5 mol/L sulfuric acid solution. (a) A current denisty
of 140mA/cm2. (b) A current density of 250 mA/cm2. (c) A current density of 300 mA/cm2.
Hence, we may name the temperature as the mode change temperature. The slope of the normalized dissolution mass
at the temperature beyond the mode change temperature decreases with the current density. This suggests that the
current consumes to generate not only the nickel ions, but also the oxygen gas with an increase in the current density.
The potential drop between the nickel anode electrode and the electric double layer increases with the current density
and causes the evolution of oxygen.
Figure 9 shows a plot of the mode change temperature vs. the current density for the 0.5 mol/L sulfuric acid solution.
Since the mode change temperature shows a very weak dependence on the current density, it is considered to be a
constant value within an experimental error. Hence, even if the high current density is applied, the mode change
temperature is not affected.
Fig. 9 A plot of the mode change temperature vs. the current demsity for the 0.5
mol/L sulfuric acid solution.
Figure 10 indicates the dependence of the mode change temperature on the concentration of sulfuric acid. The mode
change temperature decreases with the concentration of sulfuric acid as well as the transition temperature in Fig. 7. The
normalized dissolution masses at the mode change temperatures in Fig. 8 are estimated approximately at 0.15, which is
almost considered to be a constant value. Since the dissolution rate generally increases with the concentration of
sulfuric acid and temperature, the higher concentration of sulfuric acid yields the lower mode change temperature.
However, it is unclear why the surface roughening transition appears in the current pulse dissolution, but not in direct
current dissolution.
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Fig. 10
A plot of the mode change temperature vs. the concentration of sulfuric acid.
4. Conclusions
In the present work, using the confocal laser scanning microscope, the thermal surface roughening transition is found in
the anodic dissolution of nickel when the rectangular current pulse is applied. The drastic change in the dissolution mass
at the transition temperature is consistent with that in the surface roughness and is thought to correspond to the
difference in the dissolution mode, i.e., the formation of the kink-antikink or adatom-vacancy pair as the basic
excitation in the KT transition. The transition temperature decreases with the concentration of sulfuric acid. In addition,
the equivalent electric circuit model well describes the frequency-dependence of the normalized dissolution mass. In the
direct current dissolution, no transition temperature is found, however, the mode change temperature is found, which
temperature decreases with a concentration of sulfuric acid as well as the transition temperature.
Acknowledgements The author thanks Mr. Y. Esaki and Mr. K. Noguchi for their experimental set up.
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